%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA141-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:51 PM UTC 2026
% Result : Unsatisfiable 0.96s 1.18s
% Output : Proof 1.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA141-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 23:19:15 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.96/1.18 % SZS status Unsatisfiable
% 0.96/1.18 % SZS output start Proof
% 0.96/1.18 tff(b_type, type, (
% 0.96/1.18 b: ( $i * $i ) > $o)).
% 0.96/1.18 tff(s_type, type, (
% 0.96/1.18 s: $i > $i)).
% 0.96/1.18 tff(z_type, type, (
% 0.96/1.18 z: $i)).
% 0.96/1.18 tff(r_type, type, (
% 0.96/1.18 r: ( $i * $i ) > $o)).
% 0.96/1.18 tff(inj_0_type, type, (
% 0.96/1.18 inj_0: $i > $i)).
% 0.96/1.18 tff(elem_1_type, type, (
% 0.96/1.18 elem_1: $i)).
% 0.96/1.18 tff(1,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 0.96/1.18 tff(2,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 0.96/1.18 tff(3,plain,
% 0.96/1.18 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.96/1.18 inference(commutativity,[status(thm)],[])).
% 0.96/1.18 tff(4,plain,
% 0.96/1.18 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 0.96/1.18 inference(symmetry,[status(thm)],[3])).
% 0.96/1.18 tff(5,plain,
% 0.96/1.18 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[4])).
% 0.96/1.18 tff(6,plain,
% 0.96/1.18 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(7,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(8,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(9,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 0.96/1.18 tff(10,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.96/1.18 tff(11,plain,(
% 0.96/1.18 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.96/1.18 inference(skolemize,[status(sab)],[10])).
% 0.96/1.18 tff(12,plain,
% 0.96/1.18 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.96/1.18 tff(13,plain,
% 0.96/1.18 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.96/1.18 tff(14,plain,
% 0.96/1.18 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(15,plain,
% 0.96/1.18 (inj_0(s(z)) = z),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.96/1.18 tff(16,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 0.96/1.18 tff(17,plain,
% 0.96/1.18 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[16])).
% 0.96/1.18 tff(18,plain,
% 0.96/1.18 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.96/1.18 inference(symmetry,[status(thm)],[17])).
% 0.96/1.18 tff(19,plain,
% 0.96/1.18 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(20,plain,
% 0.96/1.18 (inj_0(s(s(z))) = s(z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.96/1.18 tff(21,plain,
% 0.96/1.18 (s(z) = inj_0(s(s(z)))),
% 0.96/1.18 inference(symmetry,[status(thm)],[20])).
% 0.96/1.18 tff(22,plain,
% 0.96/1.18 (s(s(z)) = s(z)),
% 0.96/1.18 inference(symmetry,[status(thm)],[16])).
% 0.96/1.18 tff(23,plain,
% 0.96/1.18 (s(s(z)) = z),
% 0.96/1.18 inference(transitivity,[status(thm)],[22, 21, 18, 15])).
% 0.96/1.18 tff(24,plain,
% 0.96/1.18 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.96/1.18 inference(bind,[status(th)],[])).
% 0.96/1.18 tff(25,plain,
% 0.96/1.18 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.96/1.18 inference(quant_intro,[status(thm)],[24])).
% 0.96/1.18 tff(26,plain,
% 0.96/1.18 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(27,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 0.96/1.18 tff(28,plain,
% 0.96/1.18 (![X: $i] : (~(s(X) = z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.96/1.18 tff(29,plain,(
% 0.96/1.18 ![X: $i] : (~(s(X) = z))),
% 0.96/1.18 inference(skolemize,[status(sab)],[28])).
% 0.96/1.18 tff(30,plain,
% 0.96/1.18 (![X: $i] : (~(s(X) = z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.96/1.18 tff(31,plain,
% 0.96/1.18 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(32,plain,
% 0.96/1.18 (~(s(s(z)) = z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.96/1.18 tff(33,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[32, 23])).
% 0.96/1.18 tff(34,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(35,plain,
% 0.96/1.18 (~(s(s(z)) = s(z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[34, 5])).
% 0.96/1.18 tff(36,plain,
% 0.96/1.18 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.96/1.18 inference(bind,[status(th)],[])).
% 0.96/1.18 tff(37,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.96/1.18 inference(quant_intro,[status(thm)],[36])).
% 0.96/1.18 tff(38,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(39,plain,
% 0.96/1.18 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.96/1.18 inference(bind,[status(th)],[])).
% 0.96/1.18 tff(40,plain,
% 0.96/1.18 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.96/1.18 inference(quant_intro,[status(thm)],[39])).
% 0.96/1.18 tff(41,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 0.96/1.18 tff(42,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.96/1.18 tff(43,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.96/1.18 tff(44,plain,(
% 0.96/1.18 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.96/1.18 inference(skolemize,[status(sab)],[43])).
% 0.96/1.18 tff(45,plain,
% 0.96/1.18 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.96/1.18 tff(46,plain,
% 0.96/1.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(47,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(48,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.96/1.18 tff(49,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[48, 45, 35, 2, 1])).
% 0.96/1.18 tff(50,plain,(b(s(s(z)), s(z)) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(51,plain,
% 0.96/1.18 (r(s(s(z)), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[50, 1])).
% 0.96/1.18 tff(52,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.96/1.18 tff(53,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.96/1.18 tff(54,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(55,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 0.96/1.18 tff(56,plain,
% 0.96/1.18 (s(z) = s(s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[55])).
% 0.96/1.18 tff(57,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(58,plain,
% 0.96/1.18 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[57])).
% 0.96/1.18 tff(59,plain,
% 0.96/1.18 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.96/1.18 inference(symmetry,[status(thm)],[58])).
% 0.96/1.18 tff(60,plain,
% 0.96/1.18 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(61,plain,
% 0.96/1.18 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[60, 13])).
% 0.96/1.18 tff(62,plain,
% 0.96/1.18 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[61])).
% 0.96/1.18 tff(63,plain,
% 0.96/1.18 (s(s(s(z))) = z),
% 0.96/1.18 inference(transitivity,[status(thm)],[62, 59, 15])).
% 0.96/1.18 tff(64,plain,
% 0.96/1.18 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(65,plain,
% 0.96/1.18 (~(s(s(s(z))) = z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[64, 30])).
% 0.96/1.18 tff(66,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[65, 63])).
% 0.96/1.18 tff(67,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(68,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[67, 56])).
% 0.96/1.18 tff(69,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(70,plain,
% 0.96/1.18 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 0.96/1.18 inference(commutativity,[status(thm)],[])).
% 0.96/1.18 tff(71,plain,
% 0.96/1.18 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[70])).
% 0.96/1.18 tff(72,plain,
% 0.96/1.18 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[71])).
% 0.96/1.18 tff(73,plain,
% 0.96/1.18 (~(z = s(s(s(z))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[65, 72])).
% 0.96/1.18 tff(74,plain,
% 0.96/1.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(75,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(76,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.96/1.18 tff(77,plain,
% 0.96/1.18 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[76, 45])).
% 0.96/1.18 tff(78,plain,
% 0.96/1.18 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[77, 73])).
% 0.96/1.18 tff(79,plain,
% 0.96/1.18 (r(z, s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[78, 54])).
% 0.96/1.18 tff(80,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(81,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.96/1.18 tff(82,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 0.96/1.18 tff(83,plain,
% 0.96/1.18 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[82])).
% 0.96/1.18 tff(84,plain,
% 0.96/1.18 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(85,plain,
% 0.96/1.18 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[84, 13])).
% 0.96/1.18 tff(86,plain,
% 0.96/1.18 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[85])).
% 0.96/1.18 tff(87,plain,
% 0.96/1.18 (s(s(s(s(z)))) = z),
% 0.96/1.18 inference(transitivity,[status(thm)],[86, 83, 15])).
% 0.96/1.18 tff(88,plain,
% 0.96/1.18 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(89,plain,
% 0.96/1.18 (~(s(s(s(s(z)))) = z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[88, 30])).
% 0.96/1.18 tff(90,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[89, 87])).
% 0.96/1.18 tff(91,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(92,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.96/1.18 tff(93,plain,
% 0.96/1.18 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 0.96/1.18 inference(commutativity,[status(thm)],[])).
% 0.96/1.18 tff(94,plain,
% 0.96/1.18 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 0.96/1.18 inference(symmetry,[status(thm)],[93])).
% 0.96/1.18 tff(95,plain,
% 0.96/1.18 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[94])).
% 0.96/1.18 tff(96,plain,
% 0.96/1.18 (~(s(s(s(s(z)))) = s(z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[67, 95])).
% 0.96/1.18 tff(97,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(98,assumption,(r(z, s(z))), introduced(assumption)).
% 0.96/1.18 tff(99,plain,
% 0.96/1.18 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.96/1.18 inference(bind,[status(th)],[])).
% 0.96/1.18 tff(100,plain,
% 0.96/1.18 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.96/1.18 inference(quant_intro,[status(thm)],[99])).
% 0.96/1.18 tff(101,plain,
% 0.96/1.18 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(102,plain,
% 0.96/1.18 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> (((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))))),
% 0.96/1.18 inference(bind,[status(th)],[])).
% 0.96/1.18 tff(103,plain,
% 0.96/1.18 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.96/1.18 inference(quant_intro,[status(thm)],[102])).
% 0.96/1.18 tff(104,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 0.96/1.18 tff(105,plain,
% 0.96/1.18 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.96/1.18 tff(106,plain,
% 0.96/1.18 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.96/1.18 tff(107,plain,(
% 0.96/1.18 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.96/1.18 inference(skolemize,[status(sab)],[106])).
% 0.96/1.18 tff(108,plain,
% 0.96/1.18 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.96/1.18 tff(109,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(110,plain,
% 0.96/1.18 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(111,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[110])).
% 0.96/1.18 tff(112,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[111, 109])).
% 0.96/1.18 tff(113,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(114,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.96/1.18 tff(115,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[114, 108, 97, 92, 52, 98])).
% 0.96/1.18 tff(116,plain,((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(117,plain,
% 0.96/1.18 (~r(z, s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[116, 97, 52, 92])).
% 0.96/1.18 tff(118,plain,
% 0.96/1.18 ((z = s(z)) <=> (s(z) = z)),
% 0.96/1.18 inference(commutativity,[status(thm)],[])).
% 0.96/1.18 tff(119,plain,
% 0.96/1.18 ((s(z) = z) <=> (z = s(z))),
% 0.96/1.18 inference(symmetry,[status(thm)],[118])).
% 0.96/1.18 tff(120,plain,
% 0.96/1.18 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[119])).
% 0.96/1.18 tff(121,plain,
% 0.96/1.18 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(122,plain,
% 0.96/1.18 (~(s(z) = z)),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[121, 30])).
% 0.96/1.18 tff(123,plain,
% 0.96/1.18 (~(z = s(z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[122, 120])).
% 0.96/1.18 tff(124,plain,
% 0.96/1.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(125,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(126,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.96/1.18 tff(127,plain,
% 0.96/1.18 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[126, 45])).
% 0.96/1.18 tff(128,plain,
% 0.96/1.18 (b(z, s(z)) | r(z, s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[127, 123])).
% 0.96/1.18 tff(129,plain,
% 0.96/1.18 (b(z, s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[128, 117])).
% 0.96/1.18 tff(130,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(131,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(132,plain,
% 0.96/1.18 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(133,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[132])).
% 0.96/1.18 tff(134,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[133, 131])).
% 0.96/1.18 tff(135,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(136,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.96/1.18 tff(137,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[136, 108, 130, 81, 92, 52])).
% 0.96/1.18 tff(138,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(139,plain,
% 0.96/1.18 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[138, 130, 52, 92])).
% 0.96/1.18 tff(140,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(141,plain,
% 0.96/1.18 (s(s(s(s(z)))) = s(s(s(z)))),
% 0.96/1.18 inference(symmetry,[status(thm)],[140])).
% 0.96/1.18 tff(142,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 0.96/1.18 tff(143,plain,
% 0.96/1.18 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 0.96/1.18 inference(commutativity,[status(thm)],[])).
% 0.96/1.18 tff(144,plain,
% 0.96/1.18 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[142])).
% 0.96/1.18 tff(145,plain,
% 0.96/1.18 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[144, 143])).
% 0.96/1.18 tff(146,plain,
% 0.96/1.18 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[145])).
% 0.96/1.18 tff(147,plain,
% 0.96/1.18 (s(s(s(s(z)))) = s(s(s(z)))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[142])).
% 0.96/1.18 tff(148,plain,
% 0.96/1.18 (s(s(s(z))) = s(s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[147])).
% 0.96/1.18 tff(149,plain,
% 0.96/1.18 (s(s(z)) = s(s(s(z)))),
% 0.96/1.18 inference(symmetry,[status(thm)],[142])).
% 0.96/1.18 tff(150,plain,
% 0.96/1.18 (s(s(z)) = s(s(s(s(z))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[149, 148])).
% 0.96/1.18 tff(151,plain,
% 0.96/1.18 (s(s(s(s(z)))) = s(s(s(z)))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.96/1.18 tff(152,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(153,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.96/1.18 tff(154,plain,((~(s(s(s(z))) = s(s(z)))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(155,plain,
% 0.96/1.18 (s(s(s(s(z)))) = s(s(s(z)))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[154, 142])).
% 0.96/1.18 tff(156,plain,
% 0.96/1.18 (s(s(s(z))) = s(s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[155])).
% 0.96/1.18 tff(157,plain,
% 0.96/1.18 (s(s(z)) = s(s(s(s(z))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[149, 156])).
% 0.96/1.18 tff(158,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 0.96/1.18 tff(159,plain,
% 0.96/1.18 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[158])).
% 0.96/1.18 tff(160,plain,
% 0.96/1.18 (s(z) = s(s(s(z)))),
% 0.96/1.18 inference(transitivity,[status(thm)],[21, 159, 61])).
% 0.96/1.18 tff(161,plain,
% 0.96/1.18 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[160])).
% 0.96/1.18 tff(162,plain,
% 0.96/1.18 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.96/1.18 inference(symmetry,[status(thm)],[161])).
% 0.96/1.18 tff(163,plain,
% 0.96/1.18 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(164,plain,
% 0.96/1.18 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[163, 13])).
% 0.96/1.18 tff(165,plain,
% 0.96/1.18 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[164])).
% 0.96/1.18 tff(166,plain,
% 0.96/1.18 (s(s(s(s(z)))) = s(s(z))),
% 0.96/1.18 inference(symmetry,[status(thm)],[158])).
% 0.96/1.18 tff(167,plain,
% 0.96/1.18 (s(s(s(s(z)))) = z),
% 0.96/1.18 inference(transitivity,[status(thm)],[166, 165, 162, 15])).
% 0.96/1.18 tff(168,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[89, 167])).
% 0.96/1.18 tff(169,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(170,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[169, 157])).
% 0.96/1.18 tff(171,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(172,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 0.96/1.18 tff(173,plain,
% 0.96/1.18 (s(s(s(z))) = s(s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[172])).
% 0.96/1.18 tff(174,plain,
% 0.96/1.18 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[173])).
% 0.96/1.18 tff(175,plain,
% 0.96/1.18 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(z))))),
% 0.96/1.18 inference(symmetry,[status(thm)],[174])).
% 0.96/1.18 tff(176,plain,
% 0.96/1.18 (s(s(s(z))) = s(s(z))),
% 0.96/1.18 inference(transitivity,[status(thm)],[62, 175, 164])).
% 0.96/1.18 tff(177,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 0.96/1.18 tff(178,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.96/1.18 tff(179,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(180,plain,
% 0.96/1.18 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[179, 171])).
% 0.96/1.18 tff(181,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[180, 141])).
% 0.96/1.18 tff(182,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(183,plain,
% 0.96/1.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(184,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(185,plain,
% 0.96/1.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.96/1.18 tff(186,plain,
% 0.96/1.18 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[185, 45, 182])).
% 0.96/1.18 tff(187,plain,
% 0.96/1.18 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[186, 139])).
% 0.96/1.18 tff(188,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.96/1.18 tff(189,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(190,plain,
% 0.96/1.18 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(rewrite,[status(thm)],[])).
% 0.96/1.18 tff(191,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.96/1.18 inference(monotonicity,[status(thm)],[190])).
% 0.96/1.18 tff(192,plain,
% 0.96/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.96/1.18 inference(transitivity,[status(thm)],[191, 189])).
% 0.96/1.18 tff(193,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.96/1.18 inference(quant_inst,[status(thm)],[])).
% 0.96/1.18 tff(194,plain,
% 0.96/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 0.96/1.18 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.96/1.18 tff(195,plain,
% 0.96/1.18 ($false),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[194, 108, 130, 92, 52, 188])).
% 0.96/1.18 tff(196,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.18 tff(197,plain,
% 0.96/1.18 (~r(s(s(s(s(z)))), s(z))),
% 0.96/1.18 inference(unit_resolution,[status(thm)],[196, 130, 92, 52])).
% 0.96/1.19 tff(198,plain,
% 0.96/1.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(199,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(200,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.96/1.19 tff(201,plain,
% 0.96/1.19 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[200, 45, 197])).
% 0.96/1.19 tff(202,plain,
% 0.96/1.19 (b(s(s(s(s(z)))), s(z))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[201, 96])).
% 0.96/1.19 tff(203,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.96/1.19 tff(204,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.96/1.19 tff(205,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(206,plain,
% 0.96/1.19 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(207,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[206])).
% 0.96/1.19 tff(208,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[207, 205])).
% 0.96/1.19 tff(209,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(210,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.96/1.19 tff(211,plain,
% 0.96/1.19 (~r(z, s(s(s(s(z)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[210, 108, 130, 97, 92])).
% 0.96/1.19 tff(212,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 0.96/1.19 tff(213,plain,
% 0.96/1.19 (s(s(s(s(z)))) = z),
% 0.96/1.19 inference(symmetry,[status(thm)],[212])).
% 0.96/1.19 tff(214,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[89, 213])).
% 0.96/1.19 tff(215,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(216,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.96/1.19 tff(217,assumption,(~b(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.96/1.19 tff(218,plain,
% 0.96/1.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(219,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(220,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.96/1.19 tff(221,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[220, 45, 217, 216, 215])).
% 0.96/1.19 tff(222,plain,(b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(223,plain,
% 0.96/1.19 (b(z, s(s(s(s(z)))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[222, 211])).
% 0.96/1.19 tff(224,plain,
% 0.96/1.19 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 0.96/1.19 inference(bind,[status(th)],[])).
% 0.96/1.19 tff(225,plain,
% 0.96/1.19 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.96/1.19 inference(quant_intro,[status(thm)],[224])).
% 0.96/1.19 tff(226,plain,
% 0.96/1.19 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(227,plain,
% 0.96/1.19 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~b(X0, X1)) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) <=> (((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))))), rewrite((((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) <=> ((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> (((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 0.96/1.19 inference(bind,[status(th)],[])).
% 0.96/1.19 tff(228,plain,
% 0.96/1.19 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.96/1.19 inference(quant_intro,[status(thm)],[227])).
% 0.96/1.19 tff(229,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 0.96/1.19 tff(230,plain,
% 0.96/1.19 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.96/1.19 tff(231,plain,
% 0.96/1.19 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.96/1.19 tff(232,plain,(
% 0.96/1.19 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.96/1.19 inference(skolemize,[status(sab)],[231])).
% 0.96/1.19 tff(233,plain,
% 0.96/1.19 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.96/1.19 tff(234,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(235,plain,
% 0.96/1.19 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(236,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[235])).
% 0.96/1.19 tff(237,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.96/1.19 inference(transitivity,[status(thm)],[236, 234])).
% 0.96/1.19 tff(238,plain,
% 0.96/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(239,plain,
% 0.96/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.96/1.19 tff(240,plain,
% 0.96/1.19 (~b(s(s(s(z))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[239, 233, 223, 53, 204])).
% 0.96/1.19 tff(241,plain,
% 0.96/1.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(242,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(243,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.96/1.19 tff(244,plain,
% 0.96/1.19 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[243, 45, 65])).
% 0.96/1.19 tff(245,plain,
% 0.96/1.19 (r(s(s(s(z))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[244, 240])).
% 0.96/1.19 tff(246,assumption,(r(s(z), z)), introduced(assumption)).
% 0.96/1.19 tff(247,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.96/1.19 tff(248,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(249,plain,
% 0.96/1.19 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(250,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[249])).
% 0.96/1.19 tff(251,plain,
% 0.96/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[250, 248])).
% 0.96/1.19 tff(252,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(253,plain,
% 0.96/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.96/1.19 tff(254,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[253, 108, 97, 247, 92, 246])).
% 0.96/1.19 tff(255,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(256,plain,
% 0.96/1.19 (~r(s(z), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[255, 245, 92, 97])).
% 0.96/1.19 tff(257,plain,
% 0.96/1.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(258,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(259,plain,
% 0.96/1.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.96/1.19 tff(260,plain,
% 0.96/1.19 (b(s(z), z) | r(s(z), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[259, 45, 122])).
% 0.96/1.19 tff(261,plain,
% 0.96/1.19 (b(s(z), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[260, 256])).
% 0.96/1.19 tff(262,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(263,plain,
% 0.96/1.19 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(264,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[263])).
% 0.96/1.19 tff(265,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.19 inference(transitivity,[status(thm)],[264, 262])).
% 0.96/1.19 tff(266,plain,
% 0.96/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(267,plain,
% 0.96/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.96/1.19 tff(268,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[267, 233, 223, 53, 261, 203])).
% 0.96/1.19 tff(269,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(270,plain,
% 0.96/1.19 (~r(z, s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[269, 202, 53, 92, 187, 130])).
% 0.96/1.19 tff(271,plain,
% 0.96/1.19 (b(z, s(s(s(z))))),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[78, 270])).
% 0.96/1.19 tff(272,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.96/1.19 tff(273,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.96/1.19 tff(274,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(275,plain,
% 0.96/1.19 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(276,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 0.96/1.19 inference(monotonicity,[status(thm)],[275])).
% 0.96/1.19 tff(277,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.96/1.19 inference(transitivity,[status(thm)],[276, 274])).
% 0.96/1.19 tff(278,plain,
% 0.96/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.96/1.19 inference(quant_inst,[status(thm)],[])).
% 0.96/1.19 tff(279,plain,
% 0.96/1.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 0.96/1.19 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.96/1.19 tff(280,plain,
% 0.96/1.19 ($false),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[279, 233, 273, 272, 53, 204])).
% 0.96/1.19 tff(281,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.19 tff(282,plain,
% 0.96/1.19 (~b(s(s(s(z))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[281, 271, 53, 187])).
% 0.96/1.19 tff(283,plain,
% 0.96/1.19 (r(s(s(s(z))), z)),
% 0.96/1.19 inference(unit_resolution,[status(thm)],[244, 282])).
% 0.96/1.19 tff(284,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.96/1.19 tff(285,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.96/1.19 tff(286,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(287,plain,
% 0.96/1.19 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 0.96/1.19 inference(rewrite,[status(thm)],[])).
% 0.96/1.19 tff(288,plain,
% 0.96/1.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[287])).
% 0.96/1.20 tff(289,plain,
% 0.96/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[288, 286])).
% 0.96/1.20 tff(290,plain,
% 0.96/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 0.96/1.20 inference(quant_inst,[status(thm)],[])).
% 0.96/1.20 tff(291,plain,
% 0.96/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 0.96/1.20 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.96/1.20 tff(292,plain,
% 0.96/1.20 (~b(s(z), z)),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[291, 233, 284, 273, 285])).
% 0.96/1.20 tff(293,plain,
% 0.96/1.20 (r(s(z), z)),
% 0.96/1.20 inference(unit_resolution,[status(thm)],[260, 292])).
% 0.96/1.20 tff(294,plain,
% 0.96/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(295,plain,
% 0.96/1.20 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.96/1.20 inference(rewrite,[status(thm)],[])).
% 0.96/1.20 tff(296,plain,
% 0.96/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.96/1.20 inference(monotonicity,[status(thm)],[295])).
% 0.96/1.20 tff(297,plain,
% 0.96/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[296, 294])).
% 0.96/1.20 tff(298,plain,
% 0.96/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 0.96/1.20 inference(quant_inst,[status(thm)],[])).
% 0.96/1.20 tff(299,plain,
% 0.96/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.04/1.20 tff(300,plain,
% 1.04/1.20 (~b(z, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[299, 233, 284, 273, 285])).
% 1.04/1.20 tff(301,plain,
% 1.04/1.20 (r(z, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[128, 300])).
% 1.04/1.20 tff(302,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(303,plain,
% 1.04/1.20 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(304,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[303])).
% 1.04/1.20 tff(305,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[304, 302])).
% 1.04/1.20 tff(306,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(307,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.04/1.20 tff(308,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[307, 108, 247, 92, 98, 246])).
% 1.04/1.20 tff(309,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(310,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[309, 301, 293, 92, 247])).
% 1.04/1.20 tff(311,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(312,plain,
% 1.04/1.20 (~b(s(z), s(s(s(z))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[311, 247, 92, 284, 273])).
% 1.04/1.20 tff(313,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.04/1.20 tff(314,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.04/1.20 tff(315,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.04/1.20 tff(316,plain,
% 1.04/1.20 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[315])).
% 1.04/1.20 tff(317,plain,
% 1.04/1.20 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.04/1.20 inference(symmetry,[status(thm)],[316])).
% 1.04/1.20 tff(318,plain,
% 1.04/1.20 (s(s(z)) = z),
% 1.04/1.20 inference(transitivity,[status(thm)],[165, 317, 15])).
% 1.04/1.20 tff(319,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[32, 318])).
% 1.04/1.20 tff(320,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(321,plain,
% 1.04/1.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(322,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(323,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[322, 321])).
% 1.04/1.20 tff(324,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[323, 45, 320, 314, 313])).
% 1.04/1.20 tff(325,plain,(r(s(z), s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(326,plain,
% 1.04/1.20 (r(s(z), s(s(s(z))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[325, 312])).
% 1.04/1.20 tff(327,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(328,plain,
% 1.04/1.20 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(329,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[328])).
% 1.04/1.20 tff(330,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[329, 327])).
% 1.04/1.20 tff(331,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(332,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[331, 330])).
% 1.04/1.20 tff(333,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[332, 108, 130, 247, 326, 52])).
% 1.04/1.20 tff(334,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(335,plain,
% 1.04/1.20 (~b(s(s(s(z))), s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[334, 283, 52, 92, 130, 271])).
% 1.04/1.20 tff(336,plain,
% 1.04/1.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(337,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(338,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.04/1.20 tff(339,plain,
% 1.04/1.20 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[338, 45])).
% 1.04/1.20 tff(340,plain,
% 1.04/1.20 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[339, 171])).
% 1.04/1.20 tff(341,plain,
% 1.04/1.20 (r(s(s(s(z))), s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[340, 335])).
% 1.04/1.20 tff(342,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(343,plain,
% 1.04/1.20 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(344,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[343])).
% 1.04/1.20 tff(345,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[344, 342])).
% 1.04/1.20 tff(346,plain,
% 1.04/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(347,plain,
% 1.04/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.04/1.20 tff(348,plain,
% 1.04/1.20 (~b(z, s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[347, 233, 80, 271, 187])).
% 1.04/1.20 tff(349,assumption,(z = s(s(z))), introduced(assumption)).
% 1.04/1.20 tff(350,plain,
% 1.04/1.20 (s(s(z)) = z),
% 1.04/1.20 inference(symmetry,[status(thm)],[349])).
% 1.04/1.20 tff(351,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[32, 350])).
% 1.04/1.20 tff(352,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(353,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.04/1.20 tff(354,assumption,(~r(z, s(s(z)))), introduced(assumption)).
% 1.04/1.20 tff(355,plain,
% 1.04/1.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(356,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(357,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[356, 355])).
% 1.04/1.20 tff(358,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[357, 45, 354, 353, 352])).
% 1.04/1.20 tff(359,plain,(r(z, s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(360,plain,
% 1.04/1.20 (r(z, s(s(z)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[359, 348])).
% 1.04/1.20 tff(361,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(362,plain,
% 1.04/1.20 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(363,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[362])).
% 1.04/1.20 tff(364,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[363, 361])).
% 1.04/1.20 tff(365,plain,
% 1.04/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(366,plain,
% 1.04/1.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[365, 364])).
% 1.04/1.20 tff(367,plain,
% 1.04/1.20 (~b(s(s(z)), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[366, 233, 80, 271, 187])).
% 1.04/1.20 tff(368,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.04/1.20 tff(369,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.04/1.20 tff(370,plain,
% 1.04/1.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(371,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(372,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[371, 370])).
% 1.04/1.20 tff(373,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[372, 45, 32, 369, 368])).
% 1.04/1.20 tff(374,plain,(r(s(s(z)), z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(375,plain,
% 1.04/1.20 (r(s(s(z)), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[374, 367])).
% 1.04/1.20 tff(376,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(377,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(378,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.04/1.20 tff(379,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[378, 108, 375, 360, 341, 283])).
% 1.04/1.20 tff(380,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(381,plain,
% 1.04/1.20 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[380, 92, 52, 53, 80])).
% 1.04/1.20 tff(382,plain,
% 1.04/1.20 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(383,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(384,plain,
% 1.04/1.20 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[383, 382])).
% 1.04/1.20 tff(385,plain,
% 1.04/1.20 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[384, 45])).
% 1.04/1.20 tff(386,plain,
% 1.04/1.20 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[385, 180])).
% 1.04/1.20 tff(387,plain,
% 1.04/1.20 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[386, 381])).
% 1.04/1.20 tff(388,assumption,(b(z, s(z))), introduced(assumption)).
% 1.04/1.20 tff(389,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.04/1.20 tff(390,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(391,plain,
% 1.04/1.20 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(392,plain,
% 1.04/1.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[391])).
% 1.04/1.21 tff(393,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[392, 390])).
% 1.04/1.21 tff(394,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(395,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[394, 393])).
% 1.04/1.21 tff(396,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[395, 233, 389, 272, 53, 388])).
% 1.04/1.21 tff(397,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(398,plain,
% 1.04/1.21 (~b(s(s(s(z))), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[397, 129, 53, 387])).
% 1.04/1.21 tff(399,plain,
% 1.04/1.21 (r(s(s(s(z))), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[244, 398])).
% 1.04/1.21 tff(400,plain,
% 1.04/1.21 (~r(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[255, 399, 92, 97])).
% 1.04/1.21 tff(401,plain,
% 1.04/1.21 (b(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[260, 400])).
% 1.04/1.21 tff(402,assumption,(b(s(z), z)), introduced(assumption)).
% 1.04/1.21 tff(403,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(404,plain,
% 1.04/1.21 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(405,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[404])).
% 1.04/1.21 tff(406,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[405, 403])).
% 1.04/1.21 tff(407,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(408,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.04/1.21 tff(409,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[408, 233, 53, 388, 402, 203])).
% 1.04/1.21 tff(410,plain,((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(411,plain,
% 1.04/1.21 (~b(s(s(s(s(z)))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[410, 401, 129, 53])).
% 1.04/1.21 tff(412,plain,
% 1.04/1.21 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[200, 45, 411])).
% 1.04/1.21 tff(413,plain,
% 1.04/1.21 (r(s(s(s(s(z)))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[412, 96])).
% 1.04/1.21 tff(414,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(415,plain,
% 1.04/1.21 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(416,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[415])).
% 1.04/1.21 tff(417,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[416, 414])).
% 1.04/1.21 tff(418,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(419,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.04/1.21 tff(420,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[419, 108, 81, 92, 52, 188])).
% 1.04/1.21 tff(421,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(422,plain,
% 1.04/1.21 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[421, 413, 92, 52])).
% 1.04/1.21 tff(423,plain,
% 1.04/1.21 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[186, 422])).
% 1.04/1.21 tff(424,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.21 tff(425,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(426,plain,
% 1.04/1.21 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(427,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[426])).
% 1.04/1.21 tff(428,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[427, 425])).
% 1.04/1.21 tff(429,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(430,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.04/1.21 tff(431,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[430, 233, 80, 424, 53, 204])).
% 1.04/1.21 tff(432,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(433,plain,
% 1.04/1.21 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[432, 423, 80, 53])).
% 1.04/1.21 tff(434,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.21 tff(435,assumption,(~r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.21 tff(436,plain,
% 1.04/1.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(437,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(438,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.04/1.21 tff(439,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[438, 45, 435, 169, 434])).
% 1.04/1.21 tff(440,plain,(r(s(s(z)), s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(441,plain,
% 1.04/1.21 (r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[440, 433])).
% 1.04/1.21 tff(442,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.04/1.21 tff(443,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(444,plain,
% 1.04/1.21 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(445,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[444])).
% 1.04/1.21 tff(446,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[445, 443])).
% 1.04/1.21 tff(447,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(448,plain,
% 1.04/1.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.04/1.21 tff(449,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[448, 233, 389, 80, 442, 204])).
% 1.04/1.21 tff(450,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(451,plain,
% 1.04/1.21 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[450, 423, 80, 387])).
% 1.04/1.21 tff(452,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.04/1.21 tff(453,plain,
% 1.04/1.21 (s(s(z)) = s(s(s(s(z))))),
% 1.04/1.21 inference(symmetry,[status(thm)],[452])).
% 1.04/1.21 tff(454,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[169, 453])).
% 1.04/1.21 tff(455,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(456,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.04/1.21 tff(457,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.04/1.21 tff(458,plain,
% 1.04/1.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(459,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(460,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.04/1.21 tff(461,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[460, 45, 457, 456, 455])).
% 1.04/1.21 tff(462,plain,(r(s(s(s(s(z)))), s(s(z))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(463,plain,
% 1.04/1.21 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[462, 451])).
% 1.04/1.21 tff(464,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(465,plain,
% 1.04/1.21 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(466,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[465])).
% 1.04/1.21 tff(467,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[466, 464])).
% 1.04/1.21 tff(468,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(469,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.04/1.21 tff(470,plain,
% 1.04/1.21 (~r(s(s(z)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[469, 108, 463, 441, 52])).
% 1.04/1.21 tff(471,plain,
% 1.04/1.21 (b(s(s(z)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[48, 45, 35, 470])).
% 1.04/1.21 tff(472,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(473,plain,
% 1.04/1.21 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(474,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[473])).
% 1.04/1.21 tff(475,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[474, 472])).
% 1.04/1.21 tff(476,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(477,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[476, 475])).
% 1.04/1.21 tff(478,plain,
% 1.04/1.21 (~r(s(z), s(s(z)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[477, 108, 463, 441, 52])).
% 1.04/1.21 tff(479,plain,
% 1.04/1.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(480,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(481,plain,
% 1.04/1.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[480, 479])).
% 1.04/1.21 tff(482,plain,
% 1.04/1.21 (b(s(z), s(s(z)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[481, 45, 34, 478])).
% 1.04/1.21 tff(483,plain,
% 1.04/1.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(484,plain,
% 1.04/1.21 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(485,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[484])).
% 1.04/1.22 tff(486,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[485, 483])).
% 1.04/1.22 tff(487,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(488,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[487, 486])).
% 1.04/1.22 tff(489,plain,
% 1.04/1.22 (~b(z, s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[488, 233, 482, 129, 471])).
% 1.04/1.22 tff(490,plain,
% 1.04/1.22 (r(z, s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[359, 489])).
% 1.04/1.22 tff(491,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.22 tff(492,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.04/1.22 tff(493,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.04/1.22 tff(494,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(495,plain,
% 1.04/1.22 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(496,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[495])).
% 1.04/1.22 tff(497,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[496, 494])).
% 1.04/1.22 tff(498,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(499,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[498, 497])).
% 1.04/1.22 tff(500,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[499, 108, 493, 492, 97, 491])).
% 1.04/1.22 tff(501,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(502,plain,
% 1.04/1.22 (~r(s(s(s(z))), s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[501, 490, 97, 441])).
% 1.04/1.22 tff(503,plain,
% 1.04/1.22 (b(s(s(s(z))), s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[340, 502])).
% 1.04/1.22 tff(504,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.04/1.22 tff(505,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.04/1.22 tff(506,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(507,plain,
% 1.04/1.22 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(508,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[507])).
% 1.04/1.22 tff(509,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[508, 506])).
% 1.04/1.22 tff(510,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(511,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[510, 509])).
% 1.04/1.22 tff(512,plain,
% 1.04/1.22 (~b(s(s(s(s(s(z))))), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[511, 233, 505, 388, 504])).
% 1.04/1.22 tff(513,plain,
% 1.04/1.22 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(514,plain,
% 1.04/1.22 (~(s(s(s(s(s(z))))) = z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[513, 30])).
% 1.04/1.22 tff(515,plain,
% 1.04/1.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(516,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(517,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.04/1.22 tff(518,plain,
% 1.04/1.22 (r(s(s(s(s(s(z))))), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[517, 45, 514, 512])).
% 1.04/1.22 tff(519,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.04/1.22 tff(520,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(521,plain,
% 1.04/1.22 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(522,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[521])).
% 1.04/1.22 tff(523,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[522, 520])).
% 1.04/1.22 tff(524,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(525,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.04/1.22 tff(526,plain,
% 1.04/1.22 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[525, 233, 284, 80, 505, 504, 519])).
% 1.04/1.22 tff(527,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.04/1.22 tff(528,plain,
% 1.04/1.22 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.04/1.22 inference(symmetry,[status(thm)],[527])).
% 1.04/1.22 tff(529,plain,
% 1.04/1.22 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[528])).
% 1.04/1.22 tff(530,plain,
% 1.04/1.22 (s(z) = s(s(s(s(z))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[21, 529, 85])).
% 1.04/1.22 tff(531,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[67, 530])).
% 1.04/1.22 tff(532,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(533,plain,
% 1.04/1.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(534,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(535,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.04/1.22 tff(536,plain,
% 1.04/1.22 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[535, 45, 532, 526])).
% 1.04/1.22 tff(537,plain,
% 1.04/1.22 (~b(z, s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[488, 233, 505, 388, 519])).
% 1.04/1.22 tff(538,plain,
% 1.04/1.22 (r(z, s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[359, 537])).
% 1.04/1.22 tff(539,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(540,plain,
% 1.04/1.22 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(541,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[540])).
% 1.04/1.22 tff(542,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[541, 539])).
% 1.04/1.22 tff(543,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(544,plain,
% 1.04/1.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.04/1.22 tff(545,plain,
% 1.04/1.22 (~b(s(s(z)), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[544, 233, 505, 388, 519])).
% 1.04/1.22 tff(546,plain,
% 1.04/1.22 (r(s(s(z)), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[374, 545])).
% 1.04/1.22 tff(547,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(548,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(549,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[548, 547])).
% 1.04/1.22 tff(550,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[549, 108, 546, 538, 536, 518])).
% 1.04/1.22 tff(551,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(552,plain,
% 1.04/1.22 (~b(s(s(s(s(s(z))))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[551, 482, 129, 503, 80, 471])).
% 1.04/1.22 tff(553,plain,
% 1.04/1.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(554,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(555,plain,
% 1.04/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[554, 553])).
% 1.04/1.22 tff(556,plain,
% 1.04/1.22 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[555, 45])).
% 1.04/1.22 tff(557,plain,
% 1.04/1.22 (r(s(s(s(s(s(z))))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[556, 552, 91])).
% 1.04/1.22 tff(558,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(559,plain,
% 1.04/1.22 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(560,plain,
% 1.04/1.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[559])).
% 1.04/1.23 tff(561,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[560, 558])).
% 1.04/1.23 tff(562,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(563,plain,
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% 1.04/1.23 inference(modus_ponens,[status(thm)],[562, 561])).
% 1.04/1.23 tff(564,plain,
% 1.04/1.23 (~b(s(z), s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[563, 233, 387, 503, 80, 482, 423])).
% 1.04/1.23 tff(565,plain,
% 1.04/1.23 (r(s(z), s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[325, 564])).
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% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(567,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(568,plain,
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% 1.04/1.23 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.04/1.23 tff(569,plain,
% 1.04/1.23 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[568, 108, 565, 557, 413])).
% 1.04/1.23 tff(570,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.23 tff(571,plain,
% 1.04/1.23 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.04/1.23 inference(symmetry,[status(thm)],[570])).
% 1.04/1.23 tff(572,plain,
% 1.04/1.23 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[571])).
% 1.04/1.23 tff(573,plain,
% 1.04/1.23 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 1.04/1.23 inference(symmetry,[status(thm)],[572])).
% 1.04/1.23 tff(574,plain,
% 1.04/1.23 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.04/1.23 inference(transitivity,[status(thm)],[86, 573, 61])).
% 1.04/1.23 tff(575,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[180, 574])).
% 1.04/1.23 tff(576,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(577,plain,
% 1.04/1.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(578,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(579,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[578, 577])).
% 1.04/1.23 tff(580,plain,
% 1.04/1.23 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[579, 45, 576, 569])).
% 1.04/1.23 tff(581,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(582,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(583,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.04/1.23 tff(584,plain,
% 1.04/1.23 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[583, 108, 565, 92, 557])).
% 1.04/1.23 tff(585,plain,
% 1.04/1.23 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.04/1.23 inference(commutativity,[status(thm)],[])).
% 1.04/1.23 tff(586,plain,
% 1.04/1.23 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.04/1.23 inference(symmetry,[status(thm)],[585])).
% 1.04/1.23 tff(587,plain,
% 1.04/1.23 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[586])).
% 1.04/1.23 tff(588,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.23 tff(589,plain,
% 1.04/1.23 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[588])).
% 1.04/1.23 tff(590,plain,
% 1.04/1.23 (s(s(z)) = s(s(s(s(z))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[165, 589, 85])).
% 1.04/1.23 tff(591,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[169, 590])).
% 1.04/1.23 tff(592,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(593,plain,
% 1.04/1.23 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[592, 587])).
% 1.04/1.23 tff(594,plain,
% 1.04/1.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(595,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(596,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.04/1.23 tff(597,plain,
% 1.04/1.23 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[596, 45])).
% 1.04/1.23 tff(598,plain,
% 1.04/1.23 (b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[597, 593])).
% 1.04/1.23 tff(599,plain,
% 1.04/1.23 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[598, 584])).
% 1.04/1.23 tff(600,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(601,plain,
% 1.04/1.23 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(602,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[601])).
% 1.04/1.23 tff(603,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[602, 600])).
% 1.04/1.23 tff(604,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(605,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[604, 603])).
% 1.04/1.23 tff(606,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[605, 233, 387, 503, 599, 580])).
% 1.04/1.23 tff(607,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(608,plain,
% 1.04/1.23 (~r(z, s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[607, 92, 80, 52, 53])).
% 1.04/1.23 tff(609,plain,
% 1.04/1.23 (b(z, s(s(s(z))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[78, 608])).
% 1.04/1.23 tff(610,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(611,plain,
% 1.04/1.23 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(612,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[611])).
% 1.04/1.23 tff(613,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[612, 610])).
% 1.04/1.23 tff(614,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(615,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.04/1.23 tff(616,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[615, 233, 389, 273, 53, 204])).
% 1.04/1.23 tff(617,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(618,plain,
% 1.04/1.23 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[617, 387, 609, 53])).
% 1.04/1.23 tff(619,plain,
% 1.04/1.23 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[186, 618])).
% 1.04/1.23 tff(620,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(621,plain,
% 1.04/1.23 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(622,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[621])).
% 1.04/1.23 tff(623,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[622, 620])).
% 1.04/1.23 tff(624,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(625,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.04/1.23 tff(626,plain,
% 1.04/1.23 (~b(s(s(s(s(z)))), z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[625, 233, 389, 273, 272])).
% 1.04/1.23 tff(627,plain,
% 1.04/1.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(628,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(629,plain,
% 1.04/1.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[628, 627])).
% 1.04/1.23 tff(630,plain,
% 1.04/1.23 (r(s(s(s(s(z)))), z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[629, 45, 89, 626])).
% 1.04/1.23 tff(631,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(632,plain,
% 1.04/1.23 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(633,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[632])).
% 1.04/1.23 tff(634,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[633, 631])).
% 1.04/1.23 tff(635,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(636,plain,
% 1.04/1.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.04/1.23 tff(637,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[636, 233, 389, 80, 442, 272])).
% 1.04/1.23 tff(638,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(639,plain,
% 1.04/1.23 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[638, 389, 80, 272])).
% 1.04/1.23 tff(640,plain,
% 1.04/1.23 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[462, 639])).
% 1.04/1.23 tff(641,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(642,plain,
% 1.04/1.23 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(643,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[642])).
% 1.04/1.23 tff(644,plain,
% 1.04/1.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.04/1.24 inference(transitivity,[status(thm)],[643, 641])).
% 1.04/1.24 tff(645,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(646,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.04/1.24 tff(647,plain,
% 1.04/1.24 (~b(z, s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[646, 233, 80, 273, 272])).
% 1.04/1.24 tff(648,plain,
% 1.04/1.24 (r(z, s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[357, 45, 647, 352])).
% 1.04/1.24 tff(649,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.04/1.24 tff(650,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(651,plain,
% 1.04/1.24 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(652,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[651])).
% 1.04/1.24 tff(653,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.04/1.24 inference(transitivity,[status(thm)],[652, 650])).
% 1.04/1.24 tff(654,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(655,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[654, 653])).
% 1.04/1.24 tff(656,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[655, 233, 80, 273, 649, 272])).
% 1.04/1.24 tff(657,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(658,plain,
% 1.04/1.24 (~b(s(s(z)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[657, 272, 80, 273])).
% 1.04/1.24 tff(659,plain,
% 1.04/1.24 (r(s(s(z)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[374, 658])).
% 1.04/1.24 tff(660,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(661,plain,
% 1.04/1.24 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(662,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[661])).
% 1.04/1.24 tff(663,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[662, 660])).
% 1.04/1.24 tff(664,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(665,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[664, 663])).
% 1.04/1.24 tff(666,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[665, 108, 659, 648, 640, 630])).
% 1.04/1.24 tff(667,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(668,plain,
% 1.04/1.24 (~b(s(s(s(z))), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[667, 609, 80, 387])).
% 1.04/1.24 tff(669,plain,
% 1.04/1.24 (r(s(s(s(z))), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[244, 668])).
% 1.04/1.24 tff(670,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(671,plain,
% 1.04/1.24 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(672,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[671])).
% 1.04/1.24 tff(673,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[672, 670])).
% 1.04/1.24 tff(674,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(675,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[674, 673])).
% 1.04/1.24 tff(676,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[675, 233, 273, 649, 442, 53])).
% 1.04/1.24 tff(677,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(678,plain,
% 1.04/1.24 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[677, 649, 273, 53])).
% 1.04/1.24 tff(679,plain,
% 1.04/1.24 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[462, 678])).
% 1.04/1.24 tff(680,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.04/1.24 tff(681,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(682,plain,
% 1.04/1.24 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(683,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[682])).
% 1.04/1.24 tff(684,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[683, 681])).
% 1.04/1.24 tff(685,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(686,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[685, 684])).
% 1.04/1.24 tff(687,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[686, 108, 492, 680, 491, 81])).
% 1.04/1.24 tff(688,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(689,plain,
% 1.04/1.24 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[688, 679, 492, 81])).
% 1.04/1.24 tff(690,plain,
% 1.04/1.24 (b(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[440, 689])).
% 1.04/1.24 tff(691,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(692,plain,
% 1.04/1.24 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(693,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[692])).
% 1.04/1.24 tff(694,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[693, 691])).
% 1.04/1.24 tff(695,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(696,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[695, 694])).
% 1.04/1.24 tff(697,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[696, 233, 273, 649, 690, 53])).
% 1.04/1.24 tff(698,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(699,plain,
% 1.04/1.24 (~b(s(s(z)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[698, 81, 53, 609, 492])).
% 1.04/1.24 tff(700,plain,
% 1.04/1.24 (r(s(s(z)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[374, 699])).
% 1.04/1.24 tff(701,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.04/1.24 tff(702,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[378, 108, 701, 493, 492, 247])).
% 1.04/1.24 tff(703,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(704,plain,
% 1.04/1.24 (~r(z, s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[703, 700, 492, 669])).
% 1.04/1.24 tff(705,plain,
% 1.04/1.24 (b(z, s(s(z)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[359, 704])).
% 1.04/1.24 tff(706,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.04/1.24 tff(707,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.04/1.24 tff(708,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(709,plain,
% 1.04/1.24 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(710,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[709])).
% 1.04/1.24 tff(711,plain,
% 1.04/1.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[710, 708])).
% 1.04/1.24 tff(712,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(713,plain,
% 1.04/1.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.04/1.24 tff(714,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[713, 233, 707, 80, 273, 706])).
% 1.04/1.24 tff(715,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(716,plain,
% 1.04/1.24 (~b(s(s(s(z))), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[715, 705, 609, 80])).
% 1.04/1.24 tff(717,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.04/1.24 tff(718,plain,
% 1.04/1.24 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(719,plain,
% 1.04/1.24 (inj_0(s(elem!1)) = elem!1),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[718, 13])).
% 1.04/1.24 tff(720,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.04/1.24 tff(721,plain,
% 1.04/1.24 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[720])).
% 1.04/1.24 tff(722,plain,
% 1.04/1.24 (z = inj_0(s(z))),
% 1.04/1.24 inference(symmetry,[status(thm)],[15])).
% 1.04/1.24 tff(723,plain,
% 1.04/1.24 (z = elem!1),
% 1.04/1.24 inference(transitivity,[status(thm)],[722, 721, 719])).
% 1.04/1.24 tff(724,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[717, 723])).
% 1.04/1.24 tff(725,plain,((~(s(z) = s(elem!1))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(726,plain,
% 1.04/1.24 (~(s(z) = s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[725, 717])).
% 1.04/1.24 tff(727,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.04/1.24 tff(728,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(729,plain,
% 1.04/1.24 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(730,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[729])).
% 1.04/1.24 tff(731,plain,
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% 1.04/1.24 inference(transitivity,[status(thm)],[730, 728])).
% 1.04/1.24 tff(732,plain,
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% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(733,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[732, 731])).
% 1.04/1.24 tff(734,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[733, 108, 81, 92, 52, 727])).
% 1.04/1.24 tff(735,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(736,plain,
% 1.04/1.24 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[735, 81, 52, 92])).
% 1.04/1.24 tff(737,plain,
% 1.04/1.24 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.04/1.24 inference(commutativity,[status(thm)],[])).
% 1.04/1.24 tff(738,plain,
% 1.04/1.24 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.04/1.24 inference(symmetry,[status(thm)],[737])).
% 1.04/1.24 tff(739,plain,
% 1.04/1.24 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[738])).
% 1.04/1.25 tff(740,plain,
% 1.04/1.25 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[576, 739])).
% 1.04/1.25 tff(741,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(742,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(743,plain,
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% 1.04/1.25 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.04/1.25 tff(744,plain,
% 1.04/1.25 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[743, 45])).
% 1.04/1.25 tff(745,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[744, 740])).
% 1.04/1.25 tff(746,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[745, 736])).
% 1.04/1.25 tff(747,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
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% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(749,plain,
% 1.04/1.25 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
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% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[749])).
% 1.04/1.25 tff(751,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[750, 748])).
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% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
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% 1.04/1.25 inference(modus_ponens,[status(thm)],[752, 751])).
% 1.04/1.25 tff(754,plain,
% 1.04/1.25 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[753, 108, 92, 52, 747])).
% 1.04/1.25 tff(755,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(756,plain,
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% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
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% 1.04/1.25 inference(modus_ponens,[status(thm)],[756, 755])).
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% 1.04/1.25 ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[757, 45])).
% 1.04/1.25 tff(759,plain,
% 1.04/1.25 (b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[758, 592])).
% 1.04/1.25 tff(760,plain,
% 1.04/1.25 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[759, 754])).
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% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(762,plain,
% 1.04/1.25 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(763,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[762])).
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% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[763, 761])).
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% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
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% 1.04/1.25 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.04/1.25 tff(767,plain,
% 1.04/1.25 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[766, 108, 92, 52, 747])).
% 1.04/1.25 tff(768,plain,
% 1.04/1.25 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[598, 767])).
% 1.04/1.25 tff(769,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
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% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(771,plain,
% 1.04/1.25 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(772,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[771])).
% 1.04/1.25 tff(773,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[772, 770])).
% 1.04/1.25 tff(774,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(775,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[774, 773])).
% 1.04/1.25 tff(776,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[775, 233, 389, 769, 768, 760])).
% 1.04/1.25 tff(777,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(778,plain,
% 1.04/1.25 (~r(s(s(s(s(s(z))))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[777, 746, 387, 92, 52])).
% 1.04/1.25 tff(779,plain,
% 1.04/1.25 (b(s(s(s(s(s(z))))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[556, 778, 91])).
% 1.04/1.25 tff(780,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.04/1.25 tff(781,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(782,plain,
% 1.04/1.25 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(783,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[782])).
% 1.04/1.25 tff(784,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[783, 781])).
% 1.04/1.25 tff(785,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(786,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.04/1.25 tff(787,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[786, 108, 780, 81, 92, 52])).
% 1.04/1.25 tff(788,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(789,plain,
% 1.04/1.25 (~r(s(s(s(s(z)))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[788, 81, 92, 52])).
% 1.04/1.25 tff(790,plain,
% 1.04/1.25 (~r(s(s(s(s(z)))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[421, 81, 92, 52])).
% 1.04/1.25 tff(791,plain,
% 1.04/1.25 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.04/1.25 inference(commutativity,[status(thm)],[])).
% 1.04/1.25 tff(792,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.04/1.25 tff(793,plain,
% 1.04/1.25 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 1.04/1.25 inference(monotonicity,[status(thm)],[792])).
% 1.04/1.25 tff(794,plain,
% 1.04/1.25 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 1.04/1.25 inference(transitivity,[status(thm)],[793, 791])).
% 1.04/1.25 tff(795,plain,
% 1.04/1.25 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(z))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[794])).
% 1.04/1.25 tff(796,plain,
% 1.04/1.25 (~(elem!1 = s(s(z)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[169, 795])).
% 1.04/1.25 tff(797,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.04/1.25 tff(798,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.04/1.25 tff(799,plain,
% 1.04/1.25 ((elem!1 = z) <=> (z = elem!1)),
% 1.04/1.25 inference(commutativity,[status(thm)],[])).
% 1.04/1.25 tff(800,plain,
% 1.04/1.25 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 1.04/1.25 inference(monotonicity,[status(thm)],[792])).
% 1.04/1.25 tff(801,plain,
% 1.04/1.25 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 1.04/1.25 inference(transitivity,[status(thm)],[800, 799])).
% 1.04/1.25 tff(802,plain,
% 1.04/1.25 ((~(s(s(s(s(z)))) = z)) <=> (~(z = elem!1))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[801])).
% 1.04/1.25 tff(803,plain,
% 1.04/1.25 (~(z = elem!1)),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[89, 802])).
% 1.04/1.25 tff(804,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 1.04/1.25 inference(monotonicity,[status(thm)],[792])).
% 1.04/1.25 tff(805,plain,
% 1.04/1.25 (b(elem!1, z)),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[53, 804])).
% 1.04/1.25 tff(806,plain,
% 1.04/1.25 (~b(s(s(s(z))), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[667, 273, 80, 389])).
% 1.04/1.25 tff(807,plain,
% 1.04/1.25 (r(s(s(s(z))), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[244, 806])).
% 1.04/1.25 tff(808,plain,
% 1.04/1.25 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.04/1.25 inference(commutativity,[status(thm)],[])).
% 1.04/1.25 tff(809,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.04/1.25 tff(810,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(811,plain,
% 1.04/1.25 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(812,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[811])).
% 1.04/1.25 tff(813,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.04/1.25 inference(transitivity,[status(thm)],[812, 810])).
% 1.04/1.25 tff(814,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(815,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[814, 813])).
% 1.04/1.25 tff(816,plain,
% 1.04/1.25 (~b(elem!1, s(s(s(s(z)))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[815, 233, 809, 273, 53])).
% 1.04/1.25 tff(817,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(818,plain,
% 1.04/1.25 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(819,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[818])).
% 1.04/1.25 tff(820,plain,
% 1.04/1.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.25 inference(transitivity,[status(thm)],[819, 817])).
% 1.04/1.25 tff(821,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(822,plain,
% 1.04/1.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.04/1.25 tff(823,plain,
% 1.04/1.25 (~b(s(s(s(s(z)))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[822, 233, 809, 273, 53])).
% 1.04/1.25 tff(824,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.04/1.25 tff(825,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[824])).
% 1.04/1.25 tff(826,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.04/1.25 inference(symmetry,[status(thm)],[825])).
% 1.04/1.25 tff(827,plain,
% 1.04/1.25 (b(s(s(s(s(z)))), elem!1)),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[389, 826])).
% 1.04/1.25 tff(828,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.04/1.25 tff(829,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[828, 827])).
% 1.04/1.25 tff(830,plain,((~(elem!1 = s(s(s(z))))) | b(s(s(s(s(z)))), elem!1) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(831,plain,
% 1.04/1.25 (~(elem!1 = s(s(s(z))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[830, 823, 389])).
% 1.04/1.25 tff(832,plain,
% 1.04/1.25 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.04/1.25 inference(commutativity,[status(thm)],[])).
% 1.04/1.25 tff(833,plain,
% 1.04/1.25 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.04/1.25 inference(symmetry,[status(thm)],[832])).
% 1.04/1.25 tff(834,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.04/1.25 tff(835,plain,
% 1.04/1.25 (elem!1 = s(s(s(z)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.04/1.25 tff(836,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.04/1.25 tff(837,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[836, 835])).
% 1.04/1.25 tff(838,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(839,plain,
% 1.04/1.25 (~(s(s(s(z))) = elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[838, 831])).
% 1.04/1.25 tff(840,plain,
% 1.04/1.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(841,plain,
% 1.04/1.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(842,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[841, 840])).
% 1.04/1.26 tff(843,plain,
% 1.04/1.26 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[842, 45])).
% 1.04/1.26 tff(844,plain,
% 1.04/1.26 (r(s(s(s(z))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[843, 839, 797])).
% 1.04/1.26 tff(845,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(846,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(847,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(848,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(849,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[848, 847])).
% 1.04/1.26 tff(850,plain,
% 1.04/1.26 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[849, 45])).
% 1.04/1.26 tff(851,plain,
% 1.04/1.26 (r(elem!1, s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[850, 846, 845])).
% 1.04/1.26 tff(852,plain,
% 1.04/1.26 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.04/1.26 inference(symmetry,[status(thm)],[808])).
% 1.04/1.26 tff(853,plain,
% 1.04/1.26 (elem!1 = s(s(s(s(z))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[792, 852])).
% 1.04/1.26 tff(854,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[846, 853])).
% 1.04/1.26 tff(855,plain,((~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(856,plain,
% 1.04/1.26 (~(s(s(s(s(z)))) = elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[855, 846])).
% 1.04/1.26 tff(857,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(858,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(859,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[858, 857])).
% 1.04/1.26 tff(860,plain,
% 1.04/1.26 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[859, 45])).
% 1.04/1.26 tff(861,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[860, 856, 828])).
% 1.04/1.26 tff(862,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.04/1.26 tff(863,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(864,plain,
% 1.04/1.26 (((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(865,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[864])).
% 1.04/1.26 tff(866,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[865, 863])).
% 1.04/1.26 tff(867,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(868,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[867, 866])).
% 1.04/1.26 tff(869,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[868, 108, 862, 861, 851, 81])).
% 1.04/1.26 tff(870,plain,((elem!1 = s(s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(871,plain,
% 1.04/1.26 (elem!1 = s(s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[870, 844, 81, 823, 816])).
% 1.04/1.26 tff(872,plain,
% 1.04/1.26 (s(s(s(s(z)))) = elem!1),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[871, 808])).
% 1.04/1.26 tff(873,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(874,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(875,plain,
% 1.04/1.26 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[874])).
% 1.04/1.26 tff(876,plain,
% 1.04/1.26 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.04/1.26 inference(symmetry,[status(thm)],[875])).
% 1.04/1.26 tff(877,plain,
% 1.04/1.26 (b(elem!1, s(s(s(z))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[389, 876])).
% 1.04/1.26 tff(878,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[873, 877])).
% 1.04/1.26 tff(879,plain,((~(elem!1 = s(s(s(s(z)))))) | b(elem!1, s(s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(880,plain,
% 1.04/1.26 (~(elem!1 = s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[879, 873, 389])).
% 1.04/1.26 tff(881,plain,
% 1.04/1.26 (~(s(s(s(s(z)))) = elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[855, 880])).
% 1.04/1.26 tff(882,plain,
% 1.04/1.26 (~(elem!1 = s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[830, 828, 389])).
% 1.04/1.26 tff(883,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(884,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(885,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[884, 883])).
% 1.04/1.26 tff(886,plain,
% 1.04/1.26 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[885, 45])).
% 1.04/1.26 tff(887,plain,
% 1.04/1.26 (r(elem!1, s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[886, 873, 882])).
% 1.04/1.26 tff(888,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(889,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(890,plain,
% 1.04/1.26 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(891,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[890])).
% 1.04/1.26 tff(892,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[891, 889])).
% 1.04/1.26 tff(893,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(894,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.04/1.26 tff(895,plain,
% 1.04/1.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[894, 108, 862, 780, 888])).
% 1.04/1.26 tff(896,plain,
% 1.04/1.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[186, 895])).
% 1.04/1.26 tff(897,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(898,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(899,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.04/1.26 tff(900,plain,
% 1.04/1.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[899, 108, 862, 780, 888])).
% 1.04/1.26 tff(901,plain,
% 1.04/1.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[386, 900])).
% 1.04/1.26 tff(902,plain,
% 1.04/1.26 (~b(s(s(s(s(z)))), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[615, 233, 901, 273, 896])).
% 1.04/1.26 tff(903,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[629, 45, 89, 902])).
% 1.04/1.26 tff(904,plain,
% 1.04/1.26 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[448, 233, 901, 80, 896])).
% 1.04/1.26 tff(905,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[462, 904])).
% 1.04/1.26 tff(906,plain,
% 1.04/1.26 (~b(z, s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[347, 233, 80, 273, 896])).
% 1.04/1.26 tff(907,plain,
% 1.04/1.26 (r(z, s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[357, 45, 906, 352])).
% 1.04/1.26 tff(908,plain,
% 1.04/1.26 (~b(s(s(z)), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[366, 233, 80, 273, 896])).
% 1.04/1.26 tff(909,plain,
% 1.04/1.26 (r(s(s(z)), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[374, 908])).
% 1.04/1.26 tff(910,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[665, 108, 909, 907, 905, 903])).
% 1.04/1.26 tff(911,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(912,plain,
% 1.04/1.26 (~r(s(s(s(s(z)))), elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[911, 887, 80, 273, 862])).
% 1.04/1.26 tff(913,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[860, 912, 881, 828])).
% 1.04/1.26 tff(914,plain,(b(elem!1, s(s(s(z)))) | b(s(s(s(s(z)))), elem!1) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(915,plain,
% 1.04/1.26 (b(elem!1, s(s(s(z))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[914, 823, 80, 273, 844, 389])).
% 1.04/1.26 tff(916,plain,
% 1.04/1.26 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[871])).
% 1.04/1.26 tff(917,plain,
% 1.04/1.26 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 1.04/1.26 inference(symmetry,[status(thm)],[916])).
% 1.04/1.26 tff(918,plain,
% 1.04/1.26 (b(s(s(z)), elem!1)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[424, 917])).
% 1.04/1.26 tff(919,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.04/1.26 tff(920,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.04/1.26 tff(921,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.04/1.26 tff(922,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(923,plain,
% 1.04/1.26 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(924,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[923])).
% 1.04/1.26 tff(925,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[924, 922])).
% 1.04/1.26 tff(926,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(927,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.04/1.26 tff(928,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[927, 233, 921, 920, 919, 706])).
% 1.04/1.26 tff(929,plain,((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(930,plain,
% 1.04/1.26 (~b(z, elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[929, 918, 706, 915])).
% 1.04/1.26 tff(931,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(932,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(933,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[932, 931])).
% 1.04/1.26 tff(934,plain,
% 1.04/1.26 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[933, 45])).
% 1.04/1.26 tff(935,plain,
% 1.04/1.26 (r(z, elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[934, 930, 717])).
% 1.04/1.26 tff(936,plain,
% 1.04/1.26 (r(z, s(s(s(s(z))))) <=> r(z, elem!1)),
% 1.04/1.26 inference(monotonicity,[status(thm)],[792])).
% 1.04/1.26 tff(937,plain,
% 1.04/1.26 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 1.04/1.26 inference(symmetry,[status(thm)],[936])).
% 1.04/1.26 tff(938,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.04/1.26 tff(939,plain,
% 1.04/1.26 (r(z, s(s(s(s(z)))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[938, 937])).
% 1.04/1.26 tff(940,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[216, 939])).
% 1.04/1.26 tff(941,plain,((~r(z, elem!1)) | r(z, s(s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(942,plain,
% 1.04/1.26 (r(z, s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[941, 935, 872])).
% 1.04/1.26 tff(943,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.04/1.26 tff(944,plain,
% 1.04/1.26 (s(z) = s(s(s(s(z))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[943, 874])).
% 1.04/1.26 tff(945,plain,
% 1.04/1.26 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[944])).
% 1.04/1.26 tff(946,plain,
% 1.04/1.26 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.04/1.26 inference(symmetry,[status(thm)],[945])).
% 1.04/1.26 tff(947,plain,
% 1.04/1.26 (s(s(s(z))) = z),
% 1.04/1.26 inference(transitivity,[status(thm)],[62, 946, 15])).
% 1.04/1.26 tff(948,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[65, 947])).
% 1.04/1.26 tff(949,plain,((~(s(z) = elem!1)) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(950,plain,
% 1.04/1.26 (~(s(z) = elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[949, 871])).
% 1.04/1.26 tff(951,plain,
% 1.04/1.26 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.04/1.26 inference(commutativity,[status(thm)],[])).
% 1.04/1.26 tff(952,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.04/1.26 tff(953,plain,
% 1.04/1.26 (s(z) = elem!1),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[952, 951])).
% 1.04/1.26 tff(954,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.04/1.26 tff(955,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[954, 953])).
% 1.04/1.26 tff(956,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(957,plain,
% 1.04/1.26 (~(elem!1 = s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[956, 950])).
% 1.04/1.26 tff(958,plain,
% 1.04/1.26 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[871])).
% 1.04/1.26 tff(959,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 1.04/1.26 inference(symmetry,[status(thm)],[958])).
% 1.04/1.26 tff(960,plain,
% 1.04/1.26 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(elem!1, s(z)))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[959])).
% 1.04/1.26 tff(961,plain,
% 1.04/1.26 (~r(elem!1, s(z))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[798, 960])).
% 1.04/1.26 tff(962,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(963,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(964,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[963, 962])).
% 1.04/1.26 tff(965,plain,
% 1.04/1.26 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[964, 45])).
% 1.04/1.26 tff(966,plain,
% 1.04/1.26 (b(elem!1, s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[965, 961, 957])).
% 1.04/1.26 tff(967,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.04/1.26 tff(968,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(969,plain,
% 1.04/1.26 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(970,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[969])).
% 1.04/1.26 tff(971,plain,
% 1.04/1.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[970, 968])).
% 1.04/1.26 tff(972,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(973,plain,
% 1.04/1.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[972, 971])).
% 1.04/1.26 tff(974,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[973, 233, 809, 706, 967, 402])).
% 1.04/1.26 tff(975,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(976,plain,
% 1.04/1.26 (~b(s(z), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[975, 966, 706, 809])).
% 1.04/1.26 tff(977,plain,
% 1.04/1.26 (r(s(z), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[260, 976])).
% 1.04/1.26 tff(978,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.26 tff(979,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(980,plain,
% 1.04/1.26 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(981,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[980])).
% 1.04/1.26 tff(982,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[981, 979])).
% 1.04/1.26 tff(983,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(984,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[983, 982])).
% 1.04/1.26 tff(985,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[984, 108, 247, 978, 92, 246])).
% 1.04/1.26 tff(986,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(987,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[986, 977, 942, 92, 807])).
% 1.04/1.26 tff(988,plain,((~b(elem!1, z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (z = elem!1) | r(s(s(s(s(z)))), s(z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(989,plain,
% 1.04/1.26 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[988, 706, 805, 803, 798, 92, 81, 80, 273, 389, 797, 53])).
% 1.04/1.26 tff(990,plain,
% 1.04/1.26 (r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[440, 989])).
% 1.04/1.26 tff(991,plain,
% 1.04/1.26 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[688, 990, 492, 81])).
% 1.04/1.26 tff(992,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[792])).
% 1.04/1.26 tff(993,plain,
% 1.04/1.26 (r(elem!1, s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.26 inference(symmetry,[status(thm)],[992])).
% 1.04/1.26 tff(994,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.04/1.26 tff(995,plain,
% 1.04/1.26 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[994, 993])).
% 1.04/1.26 tff(996,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[457, 995])).
% 1.04/1.26 tff(997,plain,((~(s(s(s(s(z)))) = elem!1)) | r(s(s(s(s(z)))), s(s(z))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(998,plain,
% 1.04/1.26 (~r(elem!1, s(s(z)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[997, 991, 792])).
% 1.04/1.27 tff(999,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(1000,plain,
% 1.04/1.27 ((z = elem!1) <=> (elem!1 = z)),
% 1.04/1.27 inference(symmetry,[status(thm)],[799])).
% 1.04/1.27 tff(1001,plain,
% 1.04/1.27 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 1.04/1.27 inference(transitivity,[status(thm)],[801, 1000])).
% 1.04/1.27 tff(1002,plain,
% 1.04/1.27 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = z))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1001])).
% 1.04/1.27 tff(1003,plain,
% 1.04/1.27 (~(elem!1 = z)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[89, 1002])).
% 1.04/1.27 tff(1004,plain,
% 1.04/1.27 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.04/1.27 inference(symmetry,[status(thm)],[791])).
% 1.04/1.27 tff(1005,plain,
% 1.04/1.27 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[794, 1004])).
% 1.04/1.27 tff(1006,plain,
% 1.04/1.27 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1005])).
% 1.04/1.27 tff(1007,plain,
% 1.04/1.27 (~(s(s(z)) = elem!1)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[169, 1006])).
% 1.04/1.27 tff(1008,plain,
% 1.04/1.27 (b(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[462, 991])).
% 1.04/1.27 tff(1009,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.04/1.27 tff(1010,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1011,plain,
% 1.04/1.27 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1012,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1011])).
% 1.04/1.27 tff(1013,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1012, 1010])).
% 1.04/1.27 tff(1014,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1015,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1014, 1013])).
% 1.04/1.27 tff(1016,plain,
% 1.04/1.27 (~b(z, elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1015, 233, 1009, 80, 706])).
% 1.04/1.27 tff(1017,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1018,plain,
% 1.04/1.27 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1019,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1018])).
% 1.04/1.27 tff(1020,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1019, 1017])).
% 1.04/1.27 tff(1021,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1022,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 1.04/1.27 tff(1023,plain,
% 1.04/1.27 (~b(elem!1, z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1022, 233, 1009, 80, 706])).
% 1.04/1.27 tff(1024,plain,
% 1.04/1.27 (b(z, s(s(s(z)))) <=> b(z, elem!1)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[834])).
% 1.04/1.27 tff(1025,plain,
% 1.04/1.27 (b(z, elem!1) <=> b(z, s(s(s(z))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[1024])).
% 1.04/1.27 tff(1026,plain,
% 1.04/1.27 ((~b(z, elem!1)) <=> (~b(z, s(s(s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1025])).
% 1.04/1.27 tff(1027,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.04/1.27 tff(1028,plain,
% 1.04/1.27 (~b(z, s(s(s(z))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 1.04/1.27 tff(1029,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[273, 1028])).
% 1.04/1.27 tff(1030,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, s(s(s(z))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1031,plain,
% 1.04/1.27 (~(s(s(s(z))) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1030, 1016, 273])).
% 1.04/1.27 tff(1032,plain,
% 1.04/1.27 (r(s(s(s(z))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[843, 1031, 797])).
% 1.04/1.27 tff(1033,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.04/1.27 tff(1034,plain,
% 1.04/1.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1035,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1036,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.04/1.27 tff(1037,plain,
% 1.04/1.27 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1036, 45])).
% 1.04/1.27 tff(1038,plain,
% 1.04/1.27 (r(elem!1, z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1037, 1003, 1033])).
% 1.04/1.27 tff(1039,plain,
% 1.04/1.27 (r(z, elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[934, 803, 1027])).
% 1.04/1.27 tff(1040,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1041,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1042,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 1.04/1.27 tff(1043,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1042, 108, 1039, 1038, 862, 247])).
% 1.04/1.27 tff(1044,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1045,plain,
% 1.04/1.27 (~(s(s(s(s(z)))) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1044, 1032, 247, 1023, 1016])).
% 1.04/1.27 tff(1046,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.04/1.27 tff(1047,plain,
% 1.04/1.27 (r(elem!1, z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1037, 1023, 1046])).
% 1.04/1.27 tff(1048,plain,
% 1.04/1.27 (s(s(s(z))) = elem!1),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[824, 832])).
% 1.04/1.27 tff(1049,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.04/1.27 tff(1050,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1049, 1048])).
% 1.04/1.27 tff(1051,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1052,plain,
% 1.04/1.27 (~(elem!1 = s(s(s(z))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1051, 1031])).
% 1.04/1.27 tff(1053,assumption,(z = elem!1), introduced(assumption)).
% 1.04/1.27 tff(1054,plain,
% 1.04/1.27 (elem!1 = z),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1053, 1000])).
% 1.04/1.27 tff(1055,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1046, 1054])).
% 1.04/1.27 tff(1056,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1057,plain,
% 1.04/1.27 (~(z = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1056, 1046])).
% 1.04/1.27 tff(1058,plain,
% 1.04/1.27 (r(z, elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[934, 1016, 1057])).
% 1.04/1.27 tff(1059,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.04/1.27 tff(1060,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1061,plain,
% 1.04/1.27 (((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1062,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1061])).
% 1.04/1.27 tff(1063,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1062, 1060])).
% 1.04/1.27 tff(1064,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1065,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 1.04/1.27 tff(1066,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1065, 108, 938, 1059, 888, 247])).
% 1.04/1.27 tff(1067,plain,((~r(s(s(s(z))), z)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1068,plain,
% 1.04/1.27 (~r(elem!1, s(s(s(z))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1067, 1058, 247, 1047])).
% 1.04/1.27 tff(1069,plain,
% 1.04/1.27 (b(elem!1, s(s(s(z))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[886, 1068, 1052])).
% 1.04/1.27 tff(1070,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.04/1.27 tff(1071,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(1072,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.04/1.27 tff(1073,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1074,plain,
% 1.04/1.27 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1075,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1074])).
% 1.04/1.27 tff(1076,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1075, 1073])).
% 1.04/1.27 tff(1077,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1078,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 1.04/1.27 tff(1079,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1078, 233, 389, 1071, 919, 1072])).
% 1.04/1.27 tff(1080,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1081,plain,
% 1.04/1.27 (~b(s(s(s(z))), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1080, 1071, 389, 919])).
% 1.04/1.27 tff(1082,plain,
% 1.04/1.27 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.04/1.27 inference(commutativity,[status(thm)],[])).
% 1.04/1.27 tff(1083,plain,
% 1.04/1.27 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.04/1.27 inference(symmetry,[status(thm)],[1082])).
% 1.04/1.27 tff(1084,plain,
% 1.04/1.27 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(z)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1083])).
% 1.04/1.27 tff(1085,plain,
% 1.04/1.27 (~(s(s(s(z))) = s(z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[320, 1084])).
% 1.04/1.27 tff(1086,plain,
% 1.04/1.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1087,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1088,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.04/1.27 tff(1089,plain,
% 1.04/1.27 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1088, 45])).
% 1.04/1.27 tff(1090,plain,
% 1.04/1.27 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1089, 1085])).
% 1.04/1.27 tff(1091,plain,
% 1.04/1.27 (r(s(s(s(z))), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1090, 1081])).
% 1.04/1.27 tff(1092,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1093,plain,
% 1.04/1.27 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1094,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1093])).
% 1.04/1.27 tff(1095,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1094, 1092])).
% 1.04/1.27 tff(1096,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(1097,plain,
% 1.04/1.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.04/1.27 tff(1098,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1097, 233, 389, 1071, 919, 204])).
% 1.04/1.27 tff(1099,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(1100,plain,
% 1.04/1.27 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1099, 1071, 389, 919])).
% 1.04/1.27 tff(1101,plain,
% 1.04/1.27 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[186, 1100])).
% 1.04/1.27 tff(1102,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(1103,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1104,plain,
% 1.04/1.27 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(1105,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[1104])).
% 1.04/1.27 tff(1106,plain,
% 1.04/1.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1105, 1103])).
% 1.04/1.28 tff(1107,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1108,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 1.04/1.28 tff(1109,plain,
% 1.04/1.28 (~b(s(s(s(s(z)))), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1108, 233, 1071, 919, 1102])).
% 1.04/1.28 tff(1110,plain,
% 1.04/1.28 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[200, 45, 1109])).
% 1.04/1.28 tff(1111,plain,
% 1.04/1.28 (r(s(s(s(s(z)))), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1110, 96])).
% 1.04/1.28 tff(1112,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1113,plain,
% 1.04/1.28 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1114,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1113])).
% 1.04/1.28 tff(1115,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1114, 1112])).
% 1.04/1.28 tff(1116,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1117,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 1.04/1.28 tff(1118,plain,
% 1.04/1.28 (~b(s(z), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1117, 233, 1071, 919, 1102])).
% 1.04/1.28 tff(1119,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1120,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1121,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 1.04/1.28 tff(1122,plain,
% 1.04/1.28 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1121, 45, 67])).
% 1.04/1.28 tff(1123,plain,
% 1.04/1.28 (r(s(z), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1122, 1118])).
% 1.04/1.28 tff(1124,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[419, 108, 81, 92, 1123, 1111])).
% 1.04/1.28 tff(1125,plain,((~b(s(z), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(1126,plain,
% 1.04/1.28 (~b(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1125, 1101, 1091, 1071, 919])).
% 1.04/1.28 tff(1127,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1128,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1129,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.04/1.28 tff(1130,plain,
% 1.04/1.28 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1129, 45])).
% 1.04/1.28 tff(1131,plain,
% 1.04/1.28 (r(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1130, 1126, 954])).
% 1.04/1.28 tff(1132,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1133,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1134,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.04/1.28 tff(1135,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1134, 108, 1059, 862, 1131, 1091])).
% 1.04/1.28 tff(1136,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(1137,plain,
% 1.04/1.28 (~b(s(s(s(s(z)))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1136, 1059, 862, 954, 919, 389])).
% 1.04/1.28 tff(1138,plain,
% 1.04/1.28 (r(s(s(s(s(z)))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[860, 1137, 1070])).
% 1.04/1.28 tff(1139,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1140,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1141,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 1.04/1.28 tff(1142,plain,
% 1.04/1.28 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1141, 108, 1059, 862, 1138])).
% 1.04/1.28 tff(1143,plain,
% 1.04/1.28 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[186, 1142])).
% 1.04/1.28 tff(1144,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1145,plain,
% 1.04/1.28 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1146,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1145])).
% 1.04/1.28 tff(1147,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1146, 1144])).
% 1.04/1.28 tff(1148,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1149,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 1.04/1.28 tff(1150,plain,
% 1.04/1.28 (~b(elem!1, s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1149, 233, 389, 919, 1143])).
% 1.04/1.28 tff(1151,plain,
% 1.04/1.28 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[852])).
% 1.04/1.28 tff(1152,plain,
% 1.04/1.28 (~(elem!1 = s(s(s(s(z)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1070, 1151])).
% 1.04/1.28 tff(1153,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1154,plain,
% 1.04/1.28 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1155,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1154])).
% 1.04/1.28 tff(1156,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1155, 1153])).
% 1.04/1.28 tff(1157,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1158,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 1.04/1.28 tff(1159,plain,
% 1.04/1.28 (~b(s(s(z)), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1158, 233, 919, 80, 1143])).
% 1.04/1.28 tff(1160,plain,
% 1.04/1.28 (~b(s(s(z)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[366, 233, 80, 273, 1143])).
% 1.04/1.28 tff(1161,plain,
% 1.04/1.28 (r(s(s(z)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[374, 1160])).
% 1.04/1.28 tff(1162,plain,
% 1.04/1.28 (~b(z, s(s(z)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[347, 233, 80, 273, 1143])).
% 1.04/1.28 tff(1163,plain,
% 1.04/1.28 (r(z, s(s(z)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[357, 45, 1162, 352])).
% 1.04/1.28 tff(1164,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1165,plain,
% 1.04/1.28 (((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1166,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1165])).
% 1.04/1.28 tff(1167,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1166, 1164])).
% 1.04/1.28 tff(1168,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1169,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 1.04/1.28 tff(1170,plain,
% 1.04/1.28 ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1169, 108])).
% 1.04/1.28 tff(1171,plain,
% 1.04/1.28 (~r(s(s(z)), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1170, 1163, 1059, 1161])).
% 1.04/1.28 tff(1172,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1173,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1174,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 1.04/1.28 tff(1175,plain,
% 1.04/1.28 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1174, 45])).
% 1.04/1.28 tff(1176,plain,
% 1.04/1.28 (s(s(z)) = elem!1),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1175, 1171, 1159])).
% 1.04/1.28 tff(1177,plain,
% 1.04/1.28 (r(z, s(s(z))) <=> r(z, elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1176])).
% 1.04/1.28 tff(1178,plain,
% 1.04/1.28 (r(z, elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1163, 1177])).
% 1.04/1.28 tff(1179,plain,
% 1.04/1.28 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.04/1.28 inference(commutativity,[status(thm)],[])).
% 1.04/1.28 tff(1180,plain,
% 1.04/1.28 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.04/1.28 inference(symmetry,[status(thm)],[1179])).
% 1.04/1.28 tff(1181,plain,
% 1.04/1.28 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1180])).
% 1.04/1.28 tff(1182,plain,
% 1.04/1.28 (~(z = s(s(s(s(z)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[89, 1181])).
% 1.04/1.28 tff(1183,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1184,plain,
% 1.04/1.28 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1185,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[1184])).
% 1.04/1.28 tff(1186,plain,
% 1.04/1.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[1185, 1183])).
% 1.04/1.28 tff(1187,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(1188,plain,
% 1.04/1.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 1.04/1.28 tff(1189,plain,
% 1.04/1.28 (~b(z, s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1188, 233, 389, 273, 1143])).
% 1.04/1.28 tff(1190,plain,
% 1.04/1.28 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[220, 45, 1189])).
% 1.04/1.28 tff(1191,plain,
% 1.04/1.28 (r(z, s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1190, 1182])).
% 1.04/1.28 tff(1192,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1193,plain,
% 1.04/1.28 (((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(1194,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1193])).
% 1.04/1.29 tff(1195,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1194, 1192])).
% 1.04/1.29 tff(1196,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1197,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 1.04/1.29 tff(1198,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1197, 108, 938, 861, 851, 978])).
% 1.04/1.29 tff(1199,plain,((elem!1 = s(s(s(s(z))))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(z)))))) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1200,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1199, 1191, 1178, 1152, 1137, 1150])).
% 1.04/1.29 tff(1201,plain,((~r(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(s(z)))) = elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1202,plain,
% 1.04/1.29 (s(z) = elem!1),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1201, 1069, 273, 389, 80, 1032, 1047, 1045])).
% 1.04/1.29 tff(1203,plain,
% 1.04/1.29 (s(s(z)) = s(elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1202])).
% 1.04/1.29 tff(1204,plain,
% 1.04/1.29 (s(s(s(z))) = s(s(elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1203])).
% 1.04/1.29 tff(1205,plain,
% 1.04/1.29 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1204])).
% 1.04/1.29 tff(1206,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1205, 1203])).
% 1.04/1.29 tff(1207,plain,
% 1.04/1.29 (b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[442, 1206])).
% 1.04/1.29 tff(1208,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1205])).
% 1.04/1.29 tff(1209,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[860, 1045, 999])).
% 1.04/1.29 tff(1210,plain,
% 1.04/1.29 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 1.04/1.29 tff(1211,plain,
% 1.04/1.29 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1203])).
% 1.04/1.29 tff(1212,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.04/1.29 tff(1213,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(1214,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1215,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1216,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 1.04/1.29 tff(1217,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1216, 108, 1059, 1213, 862, 492])).
% 1.04/1.29 tff(1218,plain,((~r(s(s(z)), elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1219,plain,
% 1.04/1.29 (~r(s(s(z)), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1218, 1032, 492, 1047])).
% 1.04/1.29 tff(1220,plain,
% 1.04/1.29 (b(s(s(z)), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1175, 1219, 1212])).
% 1.04/1.29 tff(1221,plain,
% 1.04/1.29 (b(s(elem!1), elem!1)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1220, 1211])).
% 1.04/1.29 tff(1222,plain,
% 1.04/1.29 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1204])).
% 1.04/1.29 tff(1223,plain,
% 1.04/1.29 (b(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1069, 1222])).
% 1.04/1.29 tff(1224,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1225,plain,
% 1.04/1.29 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1226,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1225])).
% 1.04/1.29 tff(1227,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1226, 1224])).
% 1.04/1.29 tff(1228,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1229,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.04/1.29 tff(1230,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1229, 233, 1223, 1221, 1210, 1207])).
% 1.04/1.29 tff(1231,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | (s(s(z)) = elem!1) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | b(s(s(s(z))), elem!1) | (elem!1 = z) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1232,plain,
% 1.04/1.29 (~b(elem!1, s(s(z)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1231, 1008, 80, 389, 273, 807, 797, 492, 1007, 1003, 999, 706])).
% 1.04/1.29 tff(1233,plain,
% 1.04/1.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1234,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1235,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.04/1.29 tff(1236,plain,
% 1.04/1.29 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1235, 45])).
% 1.04/1.29 tff(1237,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1236, 1232, 998, 796])).
% 1.04/1.29 tff(1238,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(s(z)))) | r(s(s(s(s(z)))), elem!1) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1239,plain,
% 1.04/1.29 (~(s(s(s(s(z)))) = elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1238, 716, 387, 609, 80, 492, 789, 705, 81, 790, 92, 53])).
% 1.04/1.29 tff(1240,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[860, 1239, 789])).
% 1.04/1.29 tff(1241,assumption,(s(s(s(s(s(z))))) = s(elem!1)), introduced(assumption)).
% 1.04/1.29 tff(1242,plain,
% 1.04/1.29 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1241])).
% 1.04/1.29 tff(1243,plain,
% 1.04/1.29 (s(s(s(s(z)))) = elem!1),
% 1.04/1.29 inference(transitivity,[status(thm)],[86, 1242, 719])).
% 1.04/1.29 tff(1244,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1070, 1243])).
% 1.04/1.29 tff(1245,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1246,plain,
% 1.04/1.29 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1245, 1239])).
% 1.04/1.29 tff(1247,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1248,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1249,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 1.04/1.29 tff(1250,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1249, 108, 938, 701, 492, 247])).
% 1.04/1.29 tff(1251,plain,((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1252,plain,
% 1.04/1.29 (~r(z, elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1251, 700, 492, 669])).
% 1.04/1.29 tff(1253,plain,
% 1.04/1.29 (b(z, elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[934, 717, 1252])).
% 1.04/1.29 tff(1254,plain,
% 1.04/1.29 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.04/1.29 inference(commutativity,[status(thm)],[])).
% 1.04/1.29 tff(1255,plain,
% 1.04/1.29 (s(s(s(s(z)))) = s(elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[834])).
% 1.04/1.29 tff(1256,plain,
% 1.04/1.29 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1255])).
% 1.04/1.29 tff(1257,plain,
% 1.04/1.29 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1256])).
% 1.04/1.29 tff(1258,plain,
% 1.04/1.29 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1257])).
% 1.04/1.29 tff(1259,plain,
% 1.04/1.29 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.04/1.29 inference(transitivity,[status(thm)],[1258, 1254])).
% 1.04/1.29 tff(1260,plain,
% 1.04/1.29 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1259])).
% 1.04/1.29 tff(1261,plain,
% 1.04/1.29 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1260])).
% 1.04/1.29 tff(1262,plain,
% 1.04/1.29 (elem!1 = s(s(s(z)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[838, 834])).
% 1.04/1.29 tff(1263,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 1.04/1.29 tff(1264,plain,
% 1.04/1.29 (elem!1 = s(s(s(s(s(z)))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1263])).
% 1.04/1.29 tff(1265,plain,
% 1.04/1.29 (s(s(s(z))) = elem!1),
% 1.04/1.29 inference(symmetry,[status(thm)],[824])).
% 1.04/1.29 tff(1266,plain,
% 1.04/1.29 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1265, 1264])).
% 1.04/1.29 tff(1267,plain,
% 1.04/1.29 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1266])).
% 1.04/1.29 tff(1268,plain,
% 1.04/1.29 (s(s(z)) = s(s(s(s(z))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[165, 1267, 85])).
% 1.04/1.29 tff(1269,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[169, 1268])).
% 1.04/1.29 tff(1270,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1271,plain,
% 1.04/1.29 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1270, 1262])).
% 1.04/1.29 tff(1272,plain,
% 1.04/1.29 (~(elem!1 = s(s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1271, 1261])).
% 1.04/1.29 tff(1273,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1255, 1256])).
% 1.04/1.29 tff(1274,plain,
% 1.04/1.29 (b(s(elem!1), s(s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[769, 1273])).
% 1.04/1.29 tff(1275,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1276,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1275, 1274])).
% 1.04/1.29 tff(1277,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(s(elem!1), s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1278,plain,
% 1.04/1.29 (b(s(elem!1), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1277, 834, 746])).
% 1.04/1.29 tff(1279,plain,
% 1.04/1.29 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1256])).
% 1.04/1.29 tff(1280,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[504, 1279])).
% 1.04/1.29 tff(1281,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.04/1.29 tff(1282,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1281, 1280])).
% 1.04/1.29 tff(1283,plain,((~b(s(s(s(s(s(z))))), s(z))) | b(s(s(elem!1)), s(z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1284,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1283, 834, 504])).
% 1.04/1.29 tff(1285,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1255])).
% 1.04/1.29 tff(1286,plain,
% 1.04/1.29 (b(s(elem!1), elem!1)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1071, 1285])).
% 1.04/1.29 tff(1287,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1288,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.04/1.29 tff(1289,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(1290,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1291,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1292,plain,
% 1.04/1.29 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1293,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1292])).
% 1.04/1.29 tff(1294,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1293, 1291])).
% 1.04/1.29 tff(1295,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1296,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 1.04/1.29 tff(1297,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1296, 233, 1290, 1289, 1288, 1287])).
% 1.04/1.29 tff(1298,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1299,plain,
% 1.04/1.29 (~b(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1298, 1286, 1284, 1278])).
% 1.04/1.29 tff(1300,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1301,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1302,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1303,plain,
% 1.04/1.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1304,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1305,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 1.04/1.29 tff(1306,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1305, 45, 1302, 1301, 1300])).
% 1.04/1.29 tff(1307,plain,(b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1308,plain,
% 1.04/1.29 (r(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1307, 1299, 1272])).
% 1.04/1.29 tff(1309,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.04/1.29 tff(1310,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.04/1.29 tff(1311,plain,
% 1.04/1.29 (s(z) = s(elem!1)),
% 1.04/1.29 inference(symmetry,[status(thm)],[1310])).
% 1.04/1.29 tff(1312,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1309, 1311])).
% 1.04/1.29 tff(1313,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1314,plain,
% 1.04/1.29 (~(s(elem!1) = s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1313, 1309])).
% 1.04/1.29 tff(1315,plain,
% 1.04/1.29 (r(s(s(s(s(z)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1255])).
% 1.04/1.29 tff(1316,plain,
% 1.04/1.29 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1315])).
% 1.04/1.29 tff(1317,plain,
% 1.04/1.29 (~r(s(elem!1), s(z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[790, 1316])).
% 1.04/1.29 tff(1318,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.04/1.29 tff(1319,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.04/1.29 tff(1320,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 1.04/1.29 tff(1321,plain,
% 1.04/1.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1322,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1323,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 1.04/1.29 tff(1324,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1323, 45, 1320, 1319, 1318])).
% 1.04/1.29 tff(1325,plain,(b(s(elem!1), s(z)) | r(s(elem!1), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1326,plain,
% 1.04/1.29 (b(s(elem!1), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1325, 1317, 1314])).
% 1.04/1.29 tff(1327,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.04/1.29 tff(1328,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1329,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1330,plain,
% 1.04/1.29 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1331,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1330])).
% 1.04/1.29 tff(1332,plain,
% 1.04/1.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1331, 1329])).
% 1.04/1.29 tff(1333,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1334,plain,
% 1.04/1.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.04/1.29 tff(1335,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1334, 233, 1328, 1288, 1287, 1327])).
% 1.04/1.29 tff(1336,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1337,plain,
% 1.04/1.29 (~b(s(z), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1336, 1326, 1284, 1278])).
% 1.04/1.29 tff(1338,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.04/1.29 tff(1339,plain,
% 1.04/1.29 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1338])).
% 1.04/1.29 tff(1340,plain,
% 1.04/1.29 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1339])).
% 1.04/1.29 tff(1341,plain,
% 1.04/1.29 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1342,plain,
% 1.04/1.29 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1341, 13])).
% 1.04/1.29 tff(1343,plain,
% 1.04/1.29 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1342])).
% 1.04/1.29 tff(1344,plain,
% 1.04/1.29 (s(elem!1) = z),
% 1.04/1.29 inference(transitivity,[status(thm)],[1343, 1340, 15])).
% 1.04/1.29 tff(1345,plain,
% 1.04/1.29 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1346,plain,
% 1.04/1.29 (~(s(elem!1) = z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1345, 30])).
% 1.04/1.29 tff(1347,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1346, 1344])).
% 1.04/1.29 tff(1348,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1349,plain,
% 1.04/1.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1350,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1351,plain,
% 1.04/1.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 1.04/1.29 tff(1352,plain,
% 1.04/1.29 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1351, 45, 1348])).
% 1.04/1.29 tff(1353,plain,
% 1.04/1.29 (r(s(z), s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1352, 1337])).
% 1.04/1.29 tff(1354,plain,
% 1.04/1.29 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[834])).
% 1.04/1.29 tff(1355,plain,
% 1.04/1.29 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1354])).
% 1.04/1.29 tff(1356,plain,
% 1.04/1.29 ((~r(elem!1, s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1355])).
% 1.04/1.29 tff(1357,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.04/1.29 tff(1358,plain,
% 1.04/1.29 (~r(s(s(s(z))), s(z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 1.04/1.29 tff(1359,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[92, 1358])).
% 1.04/1.29 tff(1360,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1361,plain,
% 1.04/1.29 (r(elem!1, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1360, 834, 92])).
% 1.04/1.29 tff(1362,plain,
% 1.04/1.29 (s(elem!1) = s(s(s(s(z))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1255])).
% 1.04/1.29 tff(1363,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1364,plain,
% 1.04/1.29 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1363])).
% 1.04/1.29 tff(1365,plain,
% 1.04/1.29 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1364])).
% 1.04/1.29 tff(1366,plain,
% 1.04/1.29 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(1367,plain,
% 1.04/1.29 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1366, 13])).
% 1.04/1.29 tff(1368,plain,
% 1.04/1.29 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1367])).
% 1.04/1.29 tff(1369,plain,
% 1.04/1.29 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1363])).
% 1.04/1.29 tff(1370,plain,
% 1.04/1.29 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1369, 1368, 1365, 1342, 1362])).
% 1.04/1.29 tff(1371,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.29 tff(1372,plain,
% 1.04/1.29 (s(s(s(elem!1))) = s(elem!1)),
% 1.04/1.29 inference(transitivity,[status(thm)],[1371, 1255])).
% 1.04/1.29 tff(1373,plain,
% 1.04/1.29 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1372])).
% 1.04/1.29 tff(1374,plain,
% 1.04/1.29 (s(s(s(s(s(z))))) = elem!1),
% 1.04/1.29 inference(transitivity,[status(thm)],[1256, 1368, 1373, 719])).
% 1.04/1.29 tff(1375,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1271, 1374])).
% 1.04/1.29 tff(1376,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1377,plain,
% 1.04/1.29 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1376, 834])).
% 1.04/1.29 tff(1378,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1377, 1370])).
% 1.04/1.29 tff(1379,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(1380,plain,
% 1.04/1.29 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1379, 834])).
% 1.04/1.29 tff(1381,plain,
% 1.04/1.29 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1257, 1255])).
% 1.04/1.29 tff(1382,plain,
% 1.04/1.29 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[1381])).
% 1.04/1.29 tff(1383,plain,
% 1.04/1.29 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[1382])).
% 1.04/1.29 tff(1384,assumption,(~(s(s(s(s(s(z))))) = s(elem!1))), introduced(assumption)).
% 1.04/1.29 tff(1385,plain,
% 1.04/1.29 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.04/1.29 tff(1386,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.04/1.29 tff(1387,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1388,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.04/1.29 tff(1389,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.04/1.29 tff(1390,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(1391,plain,
% 1.04/1.29 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1392,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1391])).
% 1.14/1.30 tff(1393,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1392, 1390])).
% 1.14/1.30 tff(1394,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1395,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 1.14/1.30 tff(1396,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1395, 108, 1389, 1388, 1387, 1386])).
% 1.14/1.30 tff(1397,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1398,plain,
% 1.14/1.30 (~r(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1397, 1308, 1353, 1361])).
% 1.14/1.30 tff(1399,plain,
% 1.14/1.30 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1255])).
% 1.14/1.30 tff(1400,assumption,(r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.30 tff(1401,plain,
% 1.14/1.30 (r(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 1.14/1.30 tff(1402,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.14/1.30 tff(1403,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1402, 1401])).
% 1.14/1.30 tff(1404,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | r(s(s(elem!1)), s(elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1405,plain,
% 1.14/1.30 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1404, 1398, 834])).
% 1.14/1.30 tff(1406,plain,
% 1.14/1.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1407,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1408,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 1.14/1.30 tff(1409,plain,
% 1.14/1.30 ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1408, 45])).
% 1.14/1.30 tff(1410,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1409, 1405, 1385])).
% 1.14/1.30 tff(1411,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1362])).
% 1.14/1.30 tff(1412,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(symmetry,[status(thm)],[1411])).
% 1.14/1.30 tff(1413,assumption,(b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.30 tff(1414,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 1.14/1.30 tff(1415,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.14/1.30 tff(1416,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1415, 1414])).
% 1.14/1.30 tff(1417,plain,(b(s(s(elem!1)), s(elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1418,plain,
% 1.14/1.30 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1417, 1410, 834])).
% 1.14/1.30 tff(1419,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.30 tff(1420,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1421,plain,
% 1.14/1.30 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1422,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1421])).
% 1.14/1.30 tff(1423,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1422, 1420])).
% 1.14/1.30 tff(1424,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1425,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 1.14/1.30 tff(1426,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1425, 233, 1288, 1419, 1287, 1327])).
% 1.14/1.30 tff(1427,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1428,plain,
% 1.14/1.30 (~b(s(z), s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1427, 1284, 1278, 1326])).
% 1.14/1.30 tff(1429,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.30 tff(1430,plain,
% 1.14/1.30 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1429])).
% 1.14/1.30 tff(1431,plain,
% 1.14/1.30 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.14/1.30 inference(symmetry,[status(thm)],[1430])).
% 1.14/1.30 tff(1432,plain,
% 1.14/1.30 (s(s(elem!1)) = z),
% 1.14/1.30 inference(transitivity,[status(thm)],[1368, 1431, 15])).
% 1.14/1.30 tff(1433,plain,
% 1.14/1.30 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1434,plain,
% 1.14/1.30 (~(s(s(elem!1)) = z)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1433, 30])).
% 1.14/1.30 tff(1435,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1434, 1432])).
% 1.14/1.30 tff(1436,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1437,plain,
% 1.14/1.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1438,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1439,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 1.14/1.30 tff(1440,plain,
% 1.14/1.30 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1439, 45])).
% 1.14/1.30 tff(1441,plain,
% 1.14/1.30 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1440, 1436])).
% 1.14/1.30 tff(1442,plain,
% 1.14/1.30 (r(s(z), s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1441, 1428])).
% 1.14/1.30 tff(1443,plain,
% 1.14/1.30 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1444,plain,
% 1.14/1.30 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1443, 13])).
% 1.14/1.30 tff(1445,plain,
% 1.14/1.30 (s(elem!1) = s(s(s(s(z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[824])).
% 1.14/1.30 tff(1446,plain,
% 1.14/1.30 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1445])).
% 1.14/1.30 tff(1447,plain,
% 1.14/1.30 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1446])).
% 1.14/1.30 tff(1448,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.30 tff(1449,plain,
% 1.14/1.30 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1265, 1448, 1447])).
% 1.14/1.30 tff(1450,plain,
% 1.14/1.30 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1449])).
% 1.14/1.30 tff(1451,plain,
% 1.14/1.30 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[165, 1450, 1444])).
% 1.14/1.30 tff(1452,plain,
% 1.14/1.30 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1451])).
% 1.14/1.30 tff(1453,plain,
% 1.14/1.30 (s(z) = s(s(s(s(z))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[21, 1452, 85])).
% 1.14/1.30 tff(1454,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[67, 1453])).
% 1.14/1.30 tff(1455,plain,((~(elem!1 = s(s(s(elem!1))))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1456,plain,
% 1.14/1.30 (~(elem!1 = s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1455, 1262])).
% 1.14/1.30 tff(1457,plain,
% 1.14/1.30 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1255])).
% 1.14/1.30 tff(1458,plain,
% 1.14/1.30 (b(s(elem!1), z)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[53, 1457])).
% 1.14/1.30 tff(1459,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.14/1.30 tff(1460,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.30 tff(1461,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1462,plain,
% 1.14/1.30 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1463,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1462])).
% 1.14/1.30 tff(1464,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1463, 1461])).
% 1.14/1.30 tff(1465,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1466,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 1.14/1.30 tff(1467,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1466, 233, 921, 1460, 1289, 1459])).
% 1.14/1.30 tff(1468,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1469,plain,
% 1.14/1.30 (~b(elem!1, s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1468, 1458, 921, 1286])).
% 1.14/1.30 tff(1470,plain,
% 1.14/1.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1471,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1472,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1471, 1470])).
% 1.14/1.30 tff(1473,plain,
% 1.14/1.30 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1472, 45])).
% 1.14/1.30 tff(1474,plain,
% 1.14/1.30 (r(elem!1, s(s(s(elem!1))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1473, 1469, 1456])).
% 1.14/1.30 tff(1475,plain,
% 1.14/1.30 (r(s(z), s(s(s(z)))) <=> r(s(z), elem!1)),
% 1.14/1.30 inference(monotonicity,[status(thm)],[834])).
% 1.14/1.30 tff(1476,plain,
% 1.14/1.30 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1256])).
% 1.14/1.30 tff(1477,plain,
% 1.14/1.30 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.14/1.30 inference(monotonicity,[status(thm)],[834])).
% 1.14/1.30 tff(1478,plain,
% 1.14/1.30 (b(s(z), elem!1)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[285, 1477])).
% 1.14/1.30 tff(1479,plain,
% 1.14/1.30 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.14/1.30 inference(commutativity,[status(thm)],[])).
% 1.14/1.30 tff(1480,plain,
% 1.14/1.30 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.14/1.30 inference(symmetry,[status(thm)],[1479])).
% 1.14/1.30 tff(1481,plain,
% 1.14/1.30 ((~(s(z) = s(elem!1))) <=> (~(s(elem!1) = s(z)))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1480])).
% 1.14/1.30 tff(1482,plain,
% 1.14/1.30 (~(s(elem!1) = s(z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1309, 1481])).
% 1.14/1.30 tff(1483,plain,
% 1.14/1.30 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1362])).
% 1.14/1.30 tff(1484,plain,
% 1.14/1.30 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.14/1.30 inference(symmetry,[status(thm)],[1483])).
% 1.14/1.30 tff(1485,plain,
% 1.14/1.30 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[834])).
% 1.14/1.30 tff(1486,plain,
% 1.14/1.30 (r(elem!1, s(s(s(s(z)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[81, 1485])).
% 1.14/1.30 tff(1487,plain,
% 1.14/1.30 (r(elem!1, s(elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1486, 1484])).
% 1.14/1.30 tff(1488,plain,
% 1.14/1.30 (r(elem!1, s(z))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[92, 1354])).
% 1.14/1.30 tff(1489,plain,
% 1.14/1.30 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1362])).
% 1.14/1.30 tff(1490,plain,
% 1.14/1.30 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 1.14/1.30 inference(symmetry,[status(thm)],[1489])).
% 1.14/1.30 tff(1491,plain,
% 1.14/1.30 (r(s(z), s(elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[52, 1490])).
% 1.14/1.30 tff(1492,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.14/1.30 tff(1493,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1492, 1491])).
% 1.14/1.30 tff(1494,plain,(r(s(z), s(elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1495,plain,
% 1.14/1.30 (r(s(z), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1494, 52, 834])).
% 1.14/1.30 tff(1496,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.14/1.30 tff(1497,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.14/1.30 tff(1498,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.14/1.30 tff(1499,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1500,plain,
% 1.14/1.30 (((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1501,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1500])).
% 1.14/1.30 tff(1502,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1501, 1499])).
% 1.14/1.30 tff(1503,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1504,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 1.14/1.30 tff(1505,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1504, 108, 1498, 1389, 1497, 1496])).
% 1.14/1.30 tff(1506,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(1507,plain,
% 1.14/1.30 (~r(s(elem!1), s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1506, 1495, 1488, 1487])).
% 1.14/1.30 tff(1508,plain,
% 1.14/1.30 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1323, 45, 1507])).
% 1.14/1.30 tff(1509,plain,
% 1.14/1.30 (b(s(elem!1), s(z))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1508, 1482])).
% 1.14/1.30 tff(1510,plain,
% 1.14/1.30 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[735, 52, 81, 92])).
% 1.14/1.30 tff(1511,plain,
% 1.14/1.30 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[745, 1510])).
% 1.14/1.30 tff(1512,plain,
% 1.14/1.30 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[1277, 1511, 834])).
% 1.14/1.30 tff(1513,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1514,plain,
% 1.14/1.30 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(1515,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[1514])).
% 1.14/1.30 tff(1516,plain,
% 1.14/1.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[1515, 1513])).
% 1.14/1.30 tff(1517,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(1518,plain,
% 1.14/1.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 1.14/1.31 tff(1519,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1518, 233, 1102, 1288, 1512, 1509])).
% 1.14/1.31 tff(1520,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (s(z) = s(elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1521,plain,
% 1.14/1.31 (~b(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1520, 1478, 52, 1309, 834, 81, 92])).
% 1.14/1.31 tff(1522,plain,
% 1.14/1.31 (~b(s(s(s(s(s(z))))), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1283, 1521, 834])).
% 1.14/1.31 tff(1523,plain,
% 1.14/1.31 (r(s(s(s(s(s(z))))), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[556, 1522, 91])).
% 1.14/1.31 tff(1524,plain,
% 1.14/1.31 (r(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1523, 1476])).
% 1.14/1.31 tff(1525,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.14/1.31 tff(1526,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1527,plain,
% 1.14/1.31 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1528,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1527])).
% 1.14/1.31 tff(1529,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.14/1.31 tff(1530,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1531,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.14/1.31 tff(1532,plain,
% 1.14/1.31 (~r(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1531, 108, 1488, 1495, 1525])).
% 1.14/1.31 tff(1533,plain,
% 1.14/1.31 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1257])).
% 1.14/1.31 tff(1534,plain,
% 1.14/1.31 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(symmetry,[status(thm)],[1533])).
% 1.14/1.31 tff(1535,plain,
% 1.14/1.31 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[834])).
% 1.14/1.31 tff(1536,plain,
% 1.14/1.31 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(transitivity,[status(thm)],[1535, 1534])).
% 1.14/1.31 tff(1537,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.31 tff(1538,plain,
% 1.14/1.31 (r(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.14/1.31 tff(1539,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.14/1.31 tff(1540,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1539, 1538])).
% 1.14/1.31 tff(1541,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(s(elem!1)), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1542,plain,
% 1.14/1.31 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1541, 1532, 834])).
% 1.14/1.31 tff(1543,plain,
% 1.14/1.31 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[598, 1542])).
% 1.14/1.31 tff(1544,plain,
% 1.14/1.31 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1256])).
% 1.14/1.31 tff(1545,plain,
% 1.14/1.31 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[834])).
% 1.14/1.31 tff(1546,plain,
% 1.14/1.31 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(transitivity,[status(thm)],[1545, 1544])).
% 1.14/1.31 tff(1547,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.14/1.31 tff(1548,plain,
% 1.14/1.31 (b(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.14/1.31 tff(1549,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.14/1.31 tff(1550,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1549, 1548])).
% 1.14/1.31 tff(1551,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(elem!1)), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1552,plain,
% 1.14/1.31 (b(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1551, 1543, 834])).
% 1.14/1.31 tff(1553,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1554,plain,
% 1.14/1.31 (((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(z), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1555,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1554])).
% 1.14/1.31 tff(1556,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1555, 1553])).
% 1.14/1.31 tff(1557,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1558,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1557, 1556])).
% 1.14/1.31 tff(1559,plain,
% 1.14/1.31 (~r(elem!1, s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1558, 108, 1488, 1495, 1525])).
% 1.14/1.31 tff(1560,plain,
% 1.14/1.31 (b(elem!1, s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1307, 1559, 1272])).
% 1.14/1.31 tff(1561,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1562,plain,
% 1.14/1.31 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1563,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1562])).
% 1.14/1.31 tff(1564,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1563, 1561])).
% 1.14/1.31 tff(1565,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1566,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.14/1.31 tff(1567,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1566, 233, 1560, 1289, 1552, 1512])).
% 1.14/1.31 tff(1568,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1569,plain,
% 1.14/1.31 (~r(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1568, 1286, 52, 834, 81, 92])).
% 1.14/1.31 tff(1570,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1569, 1524])).
% 1.14/1.31 tff(1571,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (s(z) = s(elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1572,plain,
% 1.14/1.31 (~b(s(z), s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1571, 834, 81, 92, 1071, 52, 1309])).
% 1.14/1.31 tff(1573,plain,
% 1.14/1.31 (r(s(z), s(s(s(z))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[325, 1572])).
% 1.14/1.31 tff(1574,plain,
% 1.14/1.31 (r(s(z), elem!1)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1573, 1475])).
% 1.14/1.31 tff(1575,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.14/1.31 tff(1576,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.31 tff(1577,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.31 tff(1578,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.14/1.31 tff(1579,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1580,plain,
% 1.14/1.31 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1581,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1580])).
% 1.14/1.31 tff(1582,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1581, 1579])).
% 1.14/1.31 tff(1583,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1584,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 1.14/1.31 tff(1585,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1584, 108, 1578, 1577, 1576, 1575])).
% 1.14/1.31 tff(1586,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1587,plain,
% 1.14/1.31 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1586, 1574, 1474, 1442])).
% 1.14/1.31 tff(1588,plain,
% 1.14/1.31 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1255])).
% 1.14/1.31 tff(1589,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.31 tff(1590,plain,
% 1.14/1.31 (r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 1.14/1.31 tff(1591,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.14/1.31 tff(1592,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1591, 1590])).
% 1.14/1.31 tff(1593,plain,((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1594,plain,
% 1.14/1.31 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1593, 1587, 834])).
% 1.14/1.31 tff(1595,plain,
% 1.14/1.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1596,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1597,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1596, 1595])).
% 1.14/1.31 tff(1598,plain,
% 1.14/1.31 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1597, 45])).
% 1.14/1.31 tff(1599,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1598, 1594, 1377])).
% 1.14/1.31 tff(1600,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1255])).
% 1.14/1.31 tff(1601,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.31 tff(1602,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 1.14/1.31 tff(1603,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.14/1.31 tff(1604,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1603, 1602])).
% 1.14/1.31 tff(1605,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1606,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1605, 1599, 834])).
% 1.14/1.31 tff(1607,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1608,plain,
% 1.14/1.31 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1609,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1608])).
% 1.14/1.31 tff(1610,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1609, 1607])).
% 1.14/1.31 tff(1611,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1612,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 1.14/1.31 tff(1613,plain,
% 1.14/1.31 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1612, 233, 1286, 1606, 1418])).
% 1.14/1.31 tff(1614,plain,
% 1.14/1.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1615,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1616,plain,
% 1.14/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 1.14/1.31 tff(1617,plain,
% 1.14/1.31 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1616, 45, 1613, 1380])).
% 1.14/1.31 tff(1618,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1619,plain,
% 1.14/1.31 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1620,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1619])).
% 1.14/1.31 tff(1621,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1620, 1618])).
% 1.14/1.31 tff(1622,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1623,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 1.14/1.31 tff(1624,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1623, 108, 1617, 1361, 1353, 1308])).
% 1.14/1.31 tff(1625,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, elem!1)) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1626,plain,
% 1.14/1.31 (~(s(s(s(z))) = elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1625, 1253, 1246, 53, 1240, 779, 81, 92, 52, 726])).
% 1.14/1.31 tff(1627,plain,
% 1.14/1.31 (r(s(s(s(z))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[843, 1626, 716])).
% 1.14/1.31 tff(1628,assumption,(elem!1 = z), introduced(assumption)).
% 1.14/1.31 tff(1629,plain,
% 1.14/1.31 (z = elem!1),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1628, 799])).
% 1.14/1.31 tff(1630,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[717, 1629])).
% 1.14/1.31 tff(1631,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(1632,plain,
% 1.14/1.31 (~(elem!1 = z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1631, 717])).
% 1.14/1.31 tff(1633,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1634,plain,
% 1.14/1.31 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(1635,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[1634])).
% 1.14/1.31 tff(1636,plain,
% 1.14/1.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[1635, 1633])).
% 1.14/1.31 tff(1637,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(1638,plain,
% 1.14/1.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 1.14/1.31 tff(1639,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1638, 233, 921, 809, 1071, 53])).
% 1.14/1.31 tff(1640,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1641,plain,
% 1.14/1.32 (~b(elem!1, z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1640, 1253, 1240, 53])).
% 1.14/1.32 tff(1642,plain,
% 1.14/1.32 (r(elem!1, z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1037, 1641, 1632])).
% 1.14/1.32 tff(1643,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1644,plain,
% 1.14/1.32 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1645,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1644])).
% 1.14/1.32 tff(1646,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1645, 1643])).
% 1.14/1.32 tff(1647,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1648,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 1.14/1.32 tff(1649,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1648, 233, 921, 1071, 53, 967])).
% 1.14/1.32 tff(1650,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1651,plain,
% 1.14/1.32 (~b(elem!1, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1650, 1253, 1240, 53])).
% 1.14/1.32 tff(1652,plain,
% 1.14/1.32 (~(elem!1 = s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1051, 1626])).
% 1.14/1.32 tff(1653,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.14/1.32 tff(1654,plain,
% 1.14/1.32 (~(elem!1 = s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[956, 954])).
% 1.14/1.32 tff(1655,plain,
% 1.14/1.32 (r(elem!1, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[965, 1654, 1653])).
% 1.14/1.32 tff(1656,plain,
% 1.14/1.32 (~b(elem!1, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1201, 954, 80, 389, 273, 1070, 1059, 862])).
% 1.14/1.32 tff(1657,plain,
% 1.14/1.32 (r(elem!1, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[886, 1656, 836])).
% 1.14/1.32 tff(1658,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1659,plain,
% 1.14/1.32 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1660,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1659])).
% 1.14/1.32 tff(1661,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1660, 1658])).
% 1.14/1.32 tff(1662,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1663,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 1.14/1.32 tff(1664,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1663, 108, 1657, 92, 52, 1655])).
% 1.14/1.32 tff(1665,plain,((s(z) = elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1666,plain,
% 1.14/1.32 (s(z) = elem!1),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1665, 1652, 52, 92, 1651, 80, 387, 609, 1239, 1642, 1627])).
% 1.14/1.32 tff(1667,plain,
% 1.14/1.32 (s(s(z)) = s(elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1666])).
% 1.14/1.32 tff(1668,plain,
% 1.14/1.32 (s(elem!1) = s(s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1667])).
% 1.14/1.32 tff(1669,plain,
% 1.14/1.32 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1668])).
% 1.14/1.32 tff(1670,plain,
% 1.14/1.32 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.14/1.32 inference(symmetry,[status(thm)],[1669])).
% 1.14/1.32 tff(1671,plain,
% 1.14/1.32 (r(s(elem!1), z)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[700, 1670])).
% 1.14/1.32 tff(1672,plain,
% 1.14/1.32 (s(s(s(z))) = s(s(elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1667])).
% 1.14/1.32 tff(1673,plain,
% 1.14/1.32 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1672, 1667])).
% 1.14/1.32 tff(1674,plain,
% 1.14/1.32 (r(s(s(elem!1)), s(elem!1))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[492, 1673])).
% 1.14/1.32 tff(1675,plain,
% 1.14/1.32 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1672])).
% 1.14/1.32 tff(1676,plain,
% 1.14/1.32 (~r(s(s(z)), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1218, 1642, 492, 1627])).
% 1.14/1.32 tff(1677,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.14/1.32 tff(1678,plain,
% 1.14/1.32 (elem!1 = s(s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1677])).
% 1.14/1.32 tff(1679,plain,
% 1.14/1.32 (s(z) = s(s(z))),
% 1.14/1.32 inference(transitivity,[status(thm)],[943, 1678])).
% 1.14/1.32 tff(1680,plain,
% 1.14/1.32 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1679])).
% 1.14/1.32 tff(1681,plain,
% 1.14/1.32 (z = elem!1),
% 1.14/1.32 inference(transitivity,[status(thm)],[722, 1680, 20, 943])).
% 1.14/1.32 tff(1682,plain,
% 1.14/1.32 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1677])).
% 1.14/1.32 tff(1683,plain,
% 1.14/1.32 ((s(s(z)) = z) <=> (z = elem!1)),
% 1.14/1.32 inference(transitivity,[status(thm)],[1682, 799])).
% 1.14/1.32 tff(1684,plain,
% 1.14/1.32 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1683])).
% 1.14/1.32 tff(1685,plain,
% 1.14/1.32 (~(z = elem!1)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[32, 1684])).
% 1.14/1.32 tff(1686,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1685, 1681])).
% 1.14/1.32 tff(1687,plain,((~(s(z) = elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1688,plain,
% 1.14/1.32 (~(s(s(z)) = elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1687, 1666])).
% 1.14/1.32 tff(1689,plain,
% 1.14/1.32 (b(s(s(z)), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1175, 1688, 1676])).
% 1.14/1.32 tff(1690,plain,
% 1.14/1.32 (~b(elem!1, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[929, 1689, 705, 1253])).
% 1.14/1.32 tff(1691,plain,
% 1.14/1.32 (r(elem!1, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[886, 1690, 1652])).
% 1.14/1.32 tff(1692,plain,
% 1.14/1.32 (r(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1691, 1675])).
% 1.14/1.32 tff(1693,plain,
% 1.14/1.32 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1667])).
% 1.14/1.32 tff(1694,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 1.14/1.32 tff(1695,plain,
% 1.14/1.32 (s(s(z)) = elem!1),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1694, 1004])).
% 1.14/1.32 tff(1696,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1212, 1695])).
% 1.14/1.32 tff(1697,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1698,plain,
% 1.14/1.32 (~(elem!1 = s(s(z)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1697, 1688])).
% 1.14/1.32 tff(1699,plain,
% 1.14/1.32 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1666])).
% 1.14/1.32 tff(1700,plain,
% 1.14/1.32 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1699])).
% 1.14/1.32 tff(1701,plain,
% 1.14/1.32 (b(s(s(z)), s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1689, 1700])).
% 1.14/1.32 tff(1702,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1703,plain,
% 1.14/1.32 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1704,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1703])).
% 1.14/1.32 tff(1705,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1704, 1702])).
% 1.14/1.32 tff(1706,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1707,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 1.14/1.32 tff(1708,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1707, 233, 921, 1009, 706, 519])).
% 1.14/1.32 tff(1709,plain,((~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1710,plain,
% 1.14/1.32 (~b(elem!1, s(s(z)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1709, 1701, 705, 1253])).
% 1.14/1.32 tff(1711,plain,
% 1.14/1.32 (r(elem!1, s(s(z)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1236, 1710, 1698])).
% 1.14/1.32 tff(1712,plain,
% 1.14/1.32 (r(elem!1, s(elem!1))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1711, 1693])).
% 1.14/1.32 tff(1713,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1714,plain,
% 1.14/1.32 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1715,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1714])).
% 1.14/1.32 tff(1716,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1715, 1713])).
% 1.14/1.32 tff(1717,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1718,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.14/1.32 tff(1719,plain,
% 1.14/1.32 (~r(s(elem!1), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1718, 108, 1712, 1692, 1674])).
% 1.14/1.32 tff(1720,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1719, 1671])).
% 1.14/1.32 tff(1721,plain,((z = elem!1) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1722,plain,
% 1.14/1.32 (z = elem!1),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1721, 81, 52, 92, 80, 53, 492])).
% 1.14/1.32 tff(1723,plain,
% 1.14/1.32 (s(z) = s(elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1053])).
% 1.14/1.32 tff(1724,plain,
% 1.14/1.32 (s(elem!1) = s(z)),
% 1.14/1.32 inference(symmetry,[status(thm)],[1723])).
% 1.14/1.32 tff(1725,plain,
% 1.14/1.32 (s(s(z)) = s(s(elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1723])).
% 1.14/1.32 tff(1726,plain,
% 1.14/1.32 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1725])).
% 1.14/1.32 tff(1727,plain,
% 1.14/1.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1726])).
% 1.14/1.32 tff(1728,plain,
% 1.14/1.32 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1727, 1724])).
% 1.14/1.32 tff(1729,plain,
% 1.14/1.32 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1728])).
% 1.14/1.32 tff(1730,plain,
% 1.14/1.32 (r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[92, 1729])).
% 1.14/1.32 tff(1731,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1591, 1730])).
% 1.14/1.32 tff(1732,plain,(r(s(s(s(elem!1))), s(elem!1)) | (~r(s(s(s(z))), s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1733,plain,
% 1.14/1.32 (r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1732, 1722, 92])).
% 1.14/1.32 tff(1734,plain,
% 1.14/1.32 (s(z) = s(elem!1)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1722])).
% 1.14/1.32 tff(1735,plain,
% 1.14/1.32 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1734])).
% 1.14/1.32 tff(1736,plain,
% 1.14/1.32 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1722])).
% 1.14/1.32 tff(1737,plain,
% 1.14/1.32 (elem!1 = z),
% 1.14/1.32 inference(symmetry,[status(thm)],[1053])).
% 1.14/1.32 tff(1738,plain,
% 1.14/1.32 (s(elem!1) = s(z)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1737])).
% 1.14/1.32 tff(1739,plain,
% 1.14/1.32 (s(z) = s(elem!1)),
% 1.14/1.32 inference(symmetry,[status(thm)],[1738])).
% 1.14/1.32 tff(1740,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.14/1.32 tff(1741,plain,
% 1.14/1.32 (elem!1 = z),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1056, 1053])).
% 1.14/1.32 tff(1742,plain,
% 1.14/1.32 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1628])).
% 1.14/1.32 tff(1743,plain,
% 1.14/1.32 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1742])).
% 1.14/1.32 tff(1744,plain,
% 1.14/1.32 (b(elem!1, s(s(s(z))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[273, 1743])).
% 1.14/1.32 tff(1745,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[873, 1744])).
% 1.14/1.32 tff(1746,plain,((~(elem!1 = z)) | b(elem!1, s(s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1747,plain,
% 1.14/1.32 (b(elem!1, s(s(s(z))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1746, 1741, 273])).
% 1.14/1.32 tff(1748,plain,
% 1.14/1.32 (~b(s(z), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1125, 1747, 92, 81, 1071])).
% 1.14/1.32 tff(1749,plain,
% 1.14/1.32 (s(z) = elem!1),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1130, 1748, 1740])).
% 1.14/1.32 tff(1750,plain,
% 1.14/1.32 (elem!1 = s(z)),
% 1.14/1.32 inference(symmetry,[status(thm)],[1749])).
% 1.14/1.32 tff(1751,plain,
% 1.14/1.32 (elem!1 = s(elem!1)),
% 1.14/1.32 inference(transitivity,[status(thm)],[1750, 1739])).
% 1.14/1.32 tff(1752,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.14/1.32 tff(1753,plain,
% 1.14/1.32 (s(elem!1) = elem!1),
% 1.14/1.32 inference(symmetry,[status(thm)],[1752])).
% 1.14/1.32 tff(1754,plain,
% 1.14/1.32 (s(elem!1) = z),
% 1.14/1.32 inference(transitivity,[status(thm)],[1753, 1737])).
% 1.14/1.32 tff(1755,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1346, 1754])).
% 1.14/1.32 tff(1756,plain,((~(elem!1 = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1757,plain,
% 1.14/1.32 (~(elem!1 = s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1756, 1053])).
% 1.14/1.32 tff(1758,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1757, 1751])).
% 1.14/1.32 tff(1759,plain,((~(z = elem!1)) | r(s(z), elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1760,plain,
% 1.14/1.32 (r(s(z), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1759, 1722, 92, 81, 1240, 609])).
% 1.14/1.32 tff(1761,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1762,plain,
% 1.14/1.32 (((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1763,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), elem!1))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1762])).
% 1.14/1.32 tff(1764,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1763, 1761])).
% 1.14/1.32 tff(1765,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1766,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.14/1.32 tff(1767,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1766, 108, 247, 1578, 92, 98])).
% 1.14/1.32 tff(1768,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1769,plain,
% 1.14/1.32 (~r(z, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1768, 1760, 669, 92])).
% 1.14/1.32 tff(1770,plain,
% 1.14/1.32 (b(z, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[128, 1769])).
% 1.14/1.32 tff(1771,plain,
% 1.14/1.32 (b(elem!1, s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1770, 1736])).
% 1.14/1.32 tff(1772,plain,
% 1.14/1.32 (s(s(z)) = s(s(elem!1))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1734])).
% 1.14/1.32 tff(1773,plain,
% 1.14/1.32 (s(s(elem!1)) = s(s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1772])).
% 1.14/1.32 tff(1774,plain,
% 1.14/1.32 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1773])).
% 1.14/1.32 tff(1775,plain,
% 1.14/1.32 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1774])).
% 1.14/1.32 tff(1776,plain,
% 1.14/1.32 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1722])).
% 1.14/1.32 tff(1777,plain,
% 1.14/1.32 (b(elem!1, s(s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[705, 1776])).
% 1.14/1.32 tff(1778,plain,
% 1.14/1.32 (b(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1777, 1775])).
% 1.14/1.32 tff(1779,plain,
% 1.14/1.32 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1772])).
% 1.14/1.32 tff(1780,plain,
% 1.14/1.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1779])).
% 1.14/1.32 tff(1781,plain,
% 1.14/1.32 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1780])).
% 1.14/1.32 tff(1782,plain,
% 1.14/1.32 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1781])).
% 1.14/1.32 tff(1783,plain,
% 1.14/1.32 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1772])).
% 1.14/1.32 tff(1784,plain,
% 1.14/1.32 (b(s(s(elem!1)), s(s(s(z))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[80, 1783])).
% 1.14/1.32 tff(1785,plain,
% 1.14/1.32 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1784, 1782])).
% 1.14/1.32 tff(1786,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.32 tff(1787,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1788,plain,
% 1.14/1.32 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(1789,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1788])).
% 1.14/1.32 tff(1790,plain,
% 1.14/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1789, 1787])).
% 1.14/1.32 tff(1791,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(1792,plain,
% 1.14/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.14/1.32 tff(1793,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1792, 233, 1290, 967, 1328, 1786])).
% 1.14/1.32 tff(1794,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(1795,plain,
% 1.14/1.32 (~b(s(z), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1794, 1785, 1778, 1771])).
% 1.14/1.32 tff(1796,plain,
% 1.14/1.32 (r(s(z), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1352, 1795])).
% 1.14/1.32 tff(1797,plain,
% 1.14/1.32 (r(s(elem!1), s(s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[1796, 1735])).
% 1.14/1.32 tff(1798,plain,
% 1.14/1.32 (s(s(elem!1)) = s(s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1725])).
% 1.14/1.32 tff(1799,plain,
% 1.14/1.32 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1727, 1798])).
% 1.14/1.32 tff(1800,plain,
% 1.14/1.32 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[1799])).
% 1.14/1.32 tff(1801,plain,
% 1.14/1.32 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[492, 1800])).
% 1.14/1.33 tff(1802,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.33 tff(1803,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1802, 1801])).
% 1.14/1.33 tff(1804,plain,(r(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(s(s(z))), s(s(z)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1805,plain,
% 1.14/1.33 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1804, 1722, 492])).
% 1.14/1.33 tff(1806,plain,
% 1.14/1.33 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1773])).
% 1.14/1.33 tff(1807,plain,
% 1.14/1.33 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(symmetry,[status(thm)],[1806])).
% 1.14/1.33 tff(1808,plain,
% 1.14/1.33 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1053])).
% 1.14/1.33 tff(1809,plain,
% 1.14/1.33 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 1.14/1.33 inference(symmetry,[status(thm)],[1808])).
% 1.14/1.33 tff(1810,plain,
% 1.14/1.33 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), z))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1809])).
% 1.14/1.33 tff(1811,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.14/1.33 tff(1812,plain,
% 1.14/1.33 (~r(s(s(z)), z)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 1.14/1.33 tff(1813,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[701, 1812])).
% 1.14/1.33 tff(1814,plain,((~(z = elem!1)) | (~r(s(s(z)), z)) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1815,plain,
% 1.14/1.33 (r(s(s(z)), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1814, 1722, 700])).
% 1.14/1.33 tff(1816,plain,
% 1.14/1.33 (r(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1815, 1807])).
% 1.14/1.33 tff(1817,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1818,plain,
% 1.14/1.33 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1819,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1818])).
% 1.14/1.33 tff(1820,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1819, 1817])).
% 1.14/1.33 tff(1821,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1822,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 1.14/1.33 tff(1823,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1822, 108, 1816, 1805, 1797, 1733])).
% 1.14/1.33 tff(1824,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1825,plain,
% 1.14/1.33 (~r(s(s(s(z))), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1824, 619, 92, 80, 52, 53])).
% 1.14/1.33 tff(1826,plain,
% 1.14/1.33 (b(s(s(s(z))), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[340, 1825])).
% 1.14/1.33 tff(1827,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1828,plain,
% 1.14/1.33 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1829,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1828])).
% 1.14/1.33 tff(1830,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1829, 1827])).
% 1.14/1.33 tff(1831,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1832,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 1.14/1.33 tff(1833,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1832, 233, 387, 1826, 609, 53])).
% 1.14/1.33 tff(1834,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1835,plain,
% 1.14/1.33 (~r(s(s(s(z))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1834, 80, 53, 52])).
% 1.14/1.33 tff(1836,plain,
% 1.14/1.33 (b(s(s(s(z))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1090, 1835])).
% 1.14/1.33 tff(1837,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1838,plain,
% 1.14/1.33 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1839,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1838])).
% 1.14/1.33 tff(1840,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1839, 1837])).
% 1.14/1.33 tff(1841,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1842,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 1.14/1.33 tff(1843,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1842, 233, 389, 80, 424, 1072])).
% 1.14/1.33 tff(1844,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1845,plain,
% 1.14/1.33 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1844, 389, 80, 1072])).
% 1.14/1.33 tff(1846,plain,
% 1.14/1.33 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[440, 1845])).
% 1.14/1.33 tff(1847,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1848,plain,
% 1.14/1.33 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1849,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1848])).
% 1.14/1.33 tff(1850,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1849, 1847])).
% 1.14/1.33 tff(1851,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1852,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1851, 1850])).
% 1.14/1.33 tff(1853,plain,
% 1.14/1.33 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1852, 233, 389, 80, 1072])).
% 1.14/1.33 tff(1854,plain,
% 1.14/1.33 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[462, 1853])).
% 1.14/1.33 tff(1855,plain,
% 1.14/1.33 (~r(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[469, 108, 1854, 1846, 52])).
% 1.14/1.33 tff(1856,plain,
% 1.14/1.33 (b(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[48, 45, 35, 1855])).
% 1.14/1.33 tff(1857,plain,
% 1.14/1.33 (~r(s(z), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[477, 108, 1854, 1846, 52])).
% 1.14/1.33 tff(1858,plain,
% 1.14/1.33 (b(s(z), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[481, 45, 34, 1857])).
% 1.14/1.33 tff(1859,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1860,plain,
% 1.14/1.33 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1861,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1860])).
% 1.14/1.33 tff(1862,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1861, 1859])).
% 1.14/1.33 tff(1863,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1864,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 1.14/1.33 tff(1865,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1864, 233, 80, 1858, 1072, 1856])).
% 1.14/1.33 tff(1866,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(1867,plain,
% 1.14/1.33 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1866, 80, 1836, 52])).
% 1.14/1.33 tff(1868,plain,
% 1.14/1.33 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[386, 1867])).
% 1.14/1.33 tff(1869,plain,
% 1.14/1.33 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[432, 204, 80, 53])).
% 1.14/1.33 tff(1870,plain,
% 1.14/1.33 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[440, 1869])).
% 1.14/1.33 tff(1871,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1872,plain,
% 1.14/1.33 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1873,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1872])).
% 1.14/1.33 tff(1874,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1873, 1871])).
% 1.14/1.33 tff(1875,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1876,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 1.14/1.33 tff(1877,plain,
% 1.14/1.33 (~r(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1876, 108, 130, 491, 52])).
% 1.14/1.33 tff(1878,plain,
% 1.14/1.33 (b(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[48, 45, 35, 1877])).
% 1.14/1.33 tff(1879,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1880,plain,
% 1.14/1.33 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1881,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[1880])).
% 1.14/1.33 tff(1882,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[1881, 1879])).
% 1.14/1.33 tff(1883,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(1884,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 1.14/1.33 tff(1885,plain,
% 1.14/1.33 (~r(s(z), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1884, 108, 130, 491, 52])).
% 1.14/1.33 tff(1886,plain,
% 1.14/1.33 (b(s(z), s(s(z)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[481, 45, 34, 1885])).
% 1.14/1.33 tff(1887,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(1888,plain,
% 1.14/1.33 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1889,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1888])).
% 1.14/1.34 tff(1890,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1889, 1887])).
% 1.14/1.34 tff(1891,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1892,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 1.14/1.34 tff(1893,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1892, 233, 284, 1886, 1072, 1878])).
% 1.14/1.34 tff(1894,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1895,plain,
% 1.14/1.34 (~b(s(s(s(z))), s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1894, 1870, 52, 1836, 130])).
% 1.14/1.34 tff(1896,plain,
% 1.14/1.34 (r(s(s(s(z))), s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[340, 1895])).
% 1.14/1.34 tff(1897,plain,
% 1.14/1.34 (~r(z, s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[501, 1896, 97, 1870])).
% 1.14/1.34 tff(1898,plain,
% 1.14/1.34 (b(z, s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[359, 1897])).
% 1.14/1.34 tff(1899,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1900,plain,
% 1.14/1.34 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1901,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1900])).
% 1.14/1.34 tff(1902,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.14/1.34 tff(1903,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1904,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.14/1.34 tff(1905,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1904, 233, 706, 272, 53, 204])).
% 1.14/1.34 tff(1906,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1907,plain,
% 1.14/1.34 (~b(s(s(s(z))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1906, 1898, 53, 204])).
% 1.14/1.34 tff(1908,plain,
% 1.14/1.34 (r(s(s(s(z))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[244, 1907])).
% 1.14/1.34 tff(1909,plain,
% 1.14/1.34 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(1910,plain,
% 1.14/1.34 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[1909])).
% 1.14/1.34 tff(1911,assumption,(~(s(s(z)) = s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.34 tff(1912,plain,
% 1.14/1.34 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[438, 45, 434])).
% 1.14/1.34 tff(1913,plain,
% 1.14/1.34 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1912, 1911])).
% 1.14/1.34 tff(1914,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1915,plain,
% 1.14/1.34 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1916,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1915])).
% 1.14/1.34 tff(1917,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.14/1.34 tff(1918,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1919,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.14/1.34 tff(1920,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1919, 108, 130, 492, 680, 491])).
% 1.14/1.34 tff(1921,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1922,plain,
% 1.14/1.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1921, 1913, 492, 130])).
% 1.14/1.34 tff(1923,plain,
% 1.14/1.34 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[460, 45, 456])).
% 1.14/1.34 tff(1924,plain,
% 1.14/1.34 (s(s(s(s(z)))) = s(s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1923, 1922])).
% 1.14/1.34 tff(1925,plain,
% 1.14/1.34 (s(s(z)) = s(s(s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1924, 1910])).
% 1.14/1.34 tff(1926,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1911, 1925])).
% 1.14/1.34 tff(1927,plain,((s(s(z)) = s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1928,plain,
% 1.14/1.34 (b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1927, 169])).
% 1.14/1.34 tff(1929,plain,
% 1.14/1.34 (b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1928, 1896, 130, 1869])).
% 1.14/1.34 tff(1930,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.34 tff(1931,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1932,plain,
% 1.14/1.34 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1933,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1932])).
% 1.14/1.34 tff(1934,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1933, 1931])).
% 1.14/1.34 tff(1935,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1936,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.14/1.34 tff(1937,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1936, 233, 649, 442, 1930, 53])).
% 1.14/1.34 tff(1938,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1939,plain,
% 1.14/1.34 (~b(z, s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1938, 442, 649, 53])).
% 1.14/1.34 tff(1940,plain,
% 1.14/1.34 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[220, 45, 1939])).
% 1.14/1.34 tff(1941,plain,
% 1.14/1.34 (r(z, s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1940, 1182])).
% 1.14/1.34 tff(1942,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1943,plain,
% 1.14/1.34 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1944,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1943])).
% 1.14/1.34 tff(1945,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1944, 1942])).
% 1.14/1.34 tff(1946,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1947,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.14/1.34 tff(1948,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1947, 108, 130, 492, 97, 978])).
% 1.14/1.34 tff(1949,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1950,plain,
% 1.14/1.34 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1949, 1941, 492, 97])).
% 1.14/1.34 tff(1951,plain,
% 1.14/1.34 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[386, 1950])).
% 1.14/1.34 tff(1952,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1852, 233, 1951, 80, 442, 1072])).
% 1.14/1.34 tff(1953,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1954,plain,
% 1.14/1.34 (~b(s(s(z)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1953, 1929, 80, 1836, 97, 1896, 53])).
% 1.14/1.34 tff(1955,plain,
% 1.14/1.34 (r(s(s(z)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[374, 1954])).
% 1.14/1.34 tff(1956,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1957,plain,
% 1.14/1.34 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1958,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1957])).
% 1.14/1.34 tff(1959,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1958, 1956])).
% 1.14/1.34 tff(1960,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1961,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1960, 1959])).
% 1.14/1.34 tff(1962,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1961, 108, 1955, 1896, 97, 1908])).
% 1.14/1.34 tff(1963,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(1964,plain,
% 1.14/1.34 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1963, 130, 53, 80, 97, 52])).
% 1.14/1.34 tff(1965,plain,
% 1.14/1.34 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[186, 1964])).
% 1.14/1.34 tff(1966,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1967,plain,
% 1.14/1.34 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1968,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1967])).
% 1.14/1.34 tff(1969,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[1968, 1966])).
% 1.14/1.34 tff(1970,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(1971,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 1.14/1.34 tff(1972,plain,
% 1.14/1.34 (~r(s(z), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1971, 108, 130, 1965, 52])).
% 1.14/1.34 tff(1973,plain,
% 1.14/1.34 (b(s(z), s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[325, 1972])).
% 1.14/1.34 tff(1974,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1975,plain,
% 1.14/1.34 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(1976,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[1975])).
% 1.14/1.34 tff(1977,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1976, 1974])).
% 1.14/1.35 tff(1978,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1979,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 1.14/1.35 tff(1980,plain,
% 1.14/1.35 (~b(s(s(z)), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1979, 233, 80, 1836, 1973])).
% 1.14/1.35 tff(1981,plain,
% 1.14/1.35 (r(s(s(z)), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[48, 45, 35, 1980])).
% 1.14/1.35 tff(1982,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.35 tff(1983,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1984,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1985,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 1.14/1.35 tff(1986,plain,
% 1.14/1.35 (~r(s(s(s(s(s(z))))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1985, 108, 130, 52, 1982])).
% 1.14/1.35 tff(1987,plain,
% 1.14/1.35 (b(s(s(s(s(s(z))))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[556, 1986, 91])).
% 1.14/1.35 tff(1988,plain,
% 1.14/1.35 (~r(s(z), s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1971, 108, 130, 81, 52])).
% 1.14/1.35 tff(1989,plain,
% 1.14/1.35 (b(s(z), s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[325, 1988])).
% 1.14/1.35 tff(1990,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1991,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(1992,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.14/1.35 tff(1993,plain,
% 1.14/1.35 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1992, 108, 130, 81, 1982])).
% 1.14/1.35 tff(1994,plain,
% 1.14/1.35 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[598, 1993])).
% 1.14/1.35 tff(1995,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1996,plain,
% 1.14/1.35 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(1997,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[1996])).
% 1.14/1.35 tff(1998,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1997, 1995])).
% 1.14/1.35 tff(1999,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2000,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1999, 1998])).
% 1.14/1.35 tff(2001,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2000, 233, 284, 1994, 1989, 1987])).
% 1.14/1.35 tff(2002,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(2003,plain,
% 1.14/1.35 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2002, 284, 130, 52, 1965])).
% 1.14/1.35 tff(2004,plain,
% 1.14/1.35 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[579, 45, 576, 2003])).
% 1.14/1.35 tff(2005,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2006,plain,
% 1.14/1.35 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2007,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2006])).
% 1.14/1.35 tff(2008,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2007, 2005])).
% 1.14/1.35 tff(2009,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2010,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 1.14/1.35 tff(2011,plain,
% 1.14/1.35 (~r(z, s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2010, 108, 130, 97, 1965])).
% 1.14/1.35 tff(2012,plain,
% 1.14/1.35 (b(z, s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[222, 2011])).
% 1.14/1.35 tff(2013,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2014,plain,
% 1.14/1.35 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2015,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2014])).
% 1.14/1.35 tff(2016,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2015, 2013])).
% 1.14/1.35 tff(2017,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2018,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.14/1.35 tff(2019,plain,
% 1.14/1.35 (~b(s(s(s(s(s(z))))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2018, 233, 2012, 53, 2004])).
% 1.14/1.35 tff(2020,plain,
% 1.14/1.35 (r(s(s(s(s(s(z))))), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[517, 45, 514, 2019])).
% 1.14/1.35 tff(2021,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.14/1.35 tff(2022,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2023,plain,
% 1.14/1.35 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2024,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2023])).
% 1.14/1.35 tff(2025,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2024, 2022])).
% 1.14/1.35 tff(2026,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2027,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2026, 2025])).
% 1.14/1.35 tff(2028,plain,
% 1.14/1.35 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2027, 108, 97, 247, 2021])).
% 1.14/1.35 tff(2029,plain,
% 1.14/1.35 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[759, 2028])).
% 1.14/1.35 tff(2030,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2031,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2032,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.14/1.35 tff(2033,plain,
% 1.14/1.35 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2032, 108, 97, 247, 2021])).
% 1.14/1.35 tff(2034,plain,
% 1.14/1.35 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[598, 2033])).
% 1.14/1.35 tff(2035,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2036,plain,
% 1.14/1.35 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2037,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2036])).
% 1.14/1.35 tff(2038,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2037, 2035])).
% 1.14/1.35 tff(2039,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2040,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 1.14/1.35 tff(2041,plain,
% 1.14/1.35 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2040, 233, 80, 2034, 2029])).
% 1.14/1.35 tff(2042,plain,
% 1.14/1.35 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[535, 45, 532, 2041])).
% 1.14/1.35 tff(2043,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2044,plain,
% 1.14/1.35 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(2045,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[2044])).
% 1.14/1.35 tff(2046,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[2045, 2043])).
% 1.14/1.35 tff(2047,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(2048,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.14/1.35 tff(2049,plain,
% 1.14/1.35 (~b(s(s(s(s(s(z))))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2048, 233, 2034, 2029, 285])).
% 1.14/1.35 tff(2050,plain,
% 1.14/1.35 (r(s(s(s(s(s(z))))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[556, 2049, 91])).
% 1.14/1.35 tff(2051,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.14/1.35 tff(2052,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2053,plain,
% 1.14/1.36 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2054,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2053])).
% 1.14/1.36 tff(2055,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2054, 2052])).
% 1.14/1.36 tff(2056,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2057,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.14/1.36 tff(2058,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2057, 108, 2051, 52, 2050, 2042])).
% 1.14/1.36 tff(2059,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2060,plain,
% 1.14/1.36 (~r(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2059, 2020, 52, 1973, 80, 97, 1981])).
% 1.14/1.36 tff(2061,plain,
% 1.14/1.36 (b(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[244, 2060])).
% 1.14/1.36 tff(2062,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2063,plain,
% 1.14/1.36 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2064,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2063])).
% 1.14/1.36 tff(2065,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2064, 2062])).
% 1.14/1.36 tff(2066,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2067,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2066, 2065])).
% 1.14/1.36 tff(2068,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2067, 233, 284, 80, 706, 272])).
% 1.14/1.36 tff(2069,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2070,plain,
% 1.14/1.36 (~b(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2069, 284, 80, 2061])).
% 1.14/1.36 tff(2071,plain,
% 1.14/1.36 (r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[359, 2070])).
% 1.14/1.36 tff(2072,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2073,plain,
% 1.14/1.36 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2074,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2073])).
% 1.14/1.36 tff(2075,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2074, 2072])).
% 1.14/1.36 tff(2076,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2077,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 1.14/1.36 tff(2078,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2077, 108, 493, 2051, 52, 98])).
% 1.14/1.36 tff(2079,plain,((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2080,plain,
% 1.14/1.36 (~r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2079, 2071, 1981, 52])).
% 1.14/1.36 tff(2081,plain,
% 1.14/1.36 (b(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[128, 2080])).
% 1.14/1.36 tff(2082,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2083,plain,
% 1.14/1.36 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2084,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2083])).
% 1.14/1.36 tff(2085,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2084, 2082])).
% 1.14/1.36 tff(2086,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2087,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 1.14/1.36 tff(2088,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2087, 233, 2061, 1836, 2081, 1973])).
% 1.14/1.36 tff(2089,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2090,plain,
% 1.14/1.36 (~b(s(s(s(z))), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2089, 130, 80, 97, 53, 52])).
% 1.14/1.36 tff(2091,plain,
% 1.14/1.36 (r(s(s(s(z))), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[340, 2090])).
% 1.14/1.36 tff(2092,plain,
% 1.14/1.36 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1953, 1072, 80, 492, 97, 649, 53])).
% 1.14/1.36 tff(2093,plain,
% 1.14/1.36 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[462, 2092])).
% 1.14/1.36 tff(2094,plain,
% 1.14/1.36 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[688, 2093, 492, 81])).
% 1.14/1.36 tff(2095,plain,
% 1.14/1.36 (b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[440, 2094])).
% 1.14/1.36 tff(2096,plain,
% 1.14/1.36 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1844, 2095, 80, 1072])).
% 1.14/1.36 tff(2097,plain,
% 1.14/1.36 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[386, 2096])).
% 1.14/1.36 tff(2098,plain,
% 1.14/1.36 (~r(z, s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1949, 2097, 492, 97])).
% 1.14/1.36 tff(2099,plain,
% 1.14/1.36 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[220, 45, 2098])).
% 1.14/1.36 tff(2100,plain,
% 1.14/1.36 (b(z, s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2099, 1182])).
% 1.14/1.36 tff(2101,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2102,plain,
% 1.14/1.36 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2103,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2102])).
% 1.14/1.36 tff(2104,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2103, 2101])).
% 1.14/1.36 tff(2105,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2106,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 1.14/1.36 tff(2107,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2106, 233, 649, 2095, 2100, 53])).
% 1.14/1.36 tff(2108,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2109,plain,
% 1.14/1.36 (~b(s(s(z)), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2108, 2091, 80, 53, 1836, 97, 1965])).
% 1.14/1.36 tff(2110,plain,
% 1.14/1.36 (r(s(s(z)), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[374, 2109])).
% 1.14/1.36 tff(2111,plain,
% 1.14/1.36 (~r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2079, 493, 2051, 52])).
% 1.14/1.36 tff(2112,plain,
% 1.14/1.36 (b(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[128, 2111])).
% 1.14/1.36 tff(2113,plain,
% 1.14/1.36 (~r(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[703, 493, 492, 701])).
% 1.14/1.36 tff(2114,plain,
% 1.14/1.36 (b(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[244, 2113])).
% 1.14/1.36 tff(2115,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2087, 233, 2114, 1072, 2112, 285])).
% 1.14/1.36 tff(2116,plain,((~r(z, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2117,plain,
% 1.14/1.36 (~r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2116, 1973, 1836, 2091, 2110, 1981, 52])).
% 1.14/1.36 tff(2118,plain,
% 1.14/1.36 (b(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[359, 2117])).
% 1.14/1.36 tff(2119,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2120,plain,
% 1.14/1.36 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2121,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2120])).
% 1.14/1.36 tff(2122,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2121, 2119])).
% 1.14/1.36 tff(2123,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2124,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.14/1.36 tff(2125,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2124, 108, 701, 2051, 52, 98])).
% 1.14/1.36 tff(2126,plain,((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2127,plain,
% 1.14/1.36 (~r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2126, 2110, 1981, 52])).
% 1.14/1.36 tff(2128,plain,
% 1.14/1.36 (b(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[128, 2127])).
% 1.14/1.36 tff(2129,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2130,plain,
% 1.14/1.36 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2131,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[2130])).
% 1.14/1.36 tff(2132,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[2131, 2129])).
% 1.14/1.36 tff(2133,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(2134,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 1.14/1.36 tff(2135,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2134, 233, 80, 706, 272, 1072, 388, 285])).
% 1.14/1.36 tff(2136,plain,((~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2137,plain,
% 1.14/1.36 (~b(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2136, 2128, 2118, 80, 1836, 1973])).
% 1.14/1.36 tff(2138,plain,
% 1.14/1.36 (r(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[244, 2137])).
% 1.14/1.36 tff(2139,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1961, 108, 2110, 2091, 97, 2138])).
% 1.14/1.36 tff(2140,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(2141,plain,
% 1.14/1.36 (~r(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2140, 1868, 80, 52, 53])).
% 1.14/1.36 tff(2142,plain,
% 1.14/1.36 (b(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[78, 2141])).
% 1.14/1.36 tff(2143,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2144,plain,
% 1.14/1.36 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(2145,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2144])).
% 1.14/1.37 tff(2146,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2145, 2143])).
% 1.14/1.37 tff(2147,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2148,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.14/1.37 tff(2149,plain,
% 1.14/1.37 (~b(s(s(z)), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2148, 233, 80, 2142, 1836])).
% 1.14/1.37 tff(2150,plain,
% 1.14/1.37 (r(s(s(z)), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[374, 2149])).
% 1.14/1.37 tff(2151,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2152,plain,
% 1.14/1.37 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2153,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2152])).
% 1.14/1.37 tff(2154,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2153, 2151])).
% 1.14/1.37 tff(2155,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2156,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 1.14/1.37 tff(2157,plain,
% 1.14/1.37 (~b(z, s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2156, 233, 80, 2142, 1836])).
% 1.14/1.37 tff(2158,plain,
% 1.14/1.37 (r(z, s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[359, 2157])).
% 1.14/1.37 tff(2159,plain,
% 1.14/1.37 (~r(s(s(s(z))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[703, 492, 2158, 2150])).
% 1.14/1.37 tff(2160,plain,
% 1.14/1.37 (b(s(s(s(z))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[244, 2159])).
% 1.14/1.37 tff(2161,plain,
% 1.14/1.37 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[281, 2160, 53, 2142])).
% 1.14/1.37 tff(2162,plain,
% 1.14/1.37 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[186, 2161])).
% 1.14/1.37 tff(2163,plain,
% 1.14/1.37 (~r(s(z), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1971, 108, 1868, 2162, 52])).
% 1.14/1.37 tff(2164,plain,
% 1.14/1.37 (b(s(z), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[325, 2163])).
% 1.14/1.37 tff(2165,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2166,plain,
% 1.14/1.37 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2167,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2166])).
% 1.14/1.37 tff(2168,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2167, 2165])).
% 1.14/1.37 tff(2169,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2170,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 1.14/1.37 tff(2171,plain,
% 1.14/1.37 (~b(s(s(z)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2170, 233, 80, 2160, 2164])).
% 1.14/1.37 tff(2172,plain,
% 1.14/1.37 (~r(s(s(z)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2116, 2164, 1836, 2158, 2150, 492, 52])).
% 1.14/1.37 tff(2173,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[48, 45, 35, 2172, 2171])).
% 1.14/1.37 tff(2174,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2175,plain,
% 1.14/1.37 (~r(s(s(s(z))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2174, 80, 52, 53])).
% 1.14/1.37 tff(2176,plain,
% 1.14/1.37 (b(s(s(s(z))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[340, 2175])).
% 1.14/1.37 tff(2177,plain,
% 1.14/1.37 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1894, 2176, 52, 1836, 1868])).
% 1.14/1.37 tff(2178,plain,
% 1.14/1.37 (b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[440, 2177])).
% 1.14/1.37 tff(2179,plain,
% 1.14/1.37 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[432, 2178, 80, 53])).
% 1.14/1.37 tff(2180,plain,
% 1.14/1.37 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[186, 2179])).
% 1.14/1.37 tff(2181,plain,
% 1.14/1.37 (~r(s(z), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1971, 108, 1868, 2180, 52])).
% 1.14/1.37 tff(2182,plain,
% 1.14/1.37 (b(s(z), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[325, 2181])).
% 1.14/1.37 tff(2183,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2184,plain,
% 1.14/1.37 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2185,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2184])).
% 1.14/1.37 tff(2186,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2185, 2183])).
% 1.14/1.37 tff(2187,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2188,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 1.14/1.37 tff(2189,plain,
% 1.14/1.37 (~b(s(s(z)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2188, 233, 2176, 80, 2182])).
% 1.14/1.37 tff(2190,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2191,plain,
% 1.14/1.37 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2192,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2191])).
% 1.14/1.37 tff(2193,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2192, 2190])).
% 1.14/1.37 tff(2194,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2195,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 1.14/1.37 tff(2196,plain,
% 1.14/1.37 (~b(s(z), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2195, 233, 273, 1072, 285])).
% 1.14/1.37 tff(2197,plain,
% 1.14/1.37 (r(s(z), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[260, 2196])).
% 1.14/1.37 tff(2198,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2199,plain,
% 1.14/1.37 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2200,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2199])).
% 1.14/1.37 tff(2201,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2200, 2198])).
% 1.14/1.37 tff(2202,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2203,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2202, 2201])).
% 1.14/1.37 tff(2204,plain,
% 1.14/1.37 (~b(z, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2203, 233, 273, 1072, 285])).
% 1.14/1.37 tff(2205,plain,
% 1.14/1.37 (r(z, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[128, 2204])).
% 1.14/1.37 tff(2206,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2207,plain,
% 1.14/1.37 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2208,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[2207])).
% 1.14/1.37 tff(2209,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[2208, 2206])).
% 1.14/1.37 tff(2210,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2211,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 1.14/1.37 tff(2212,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2211, 108, 701, 2051, 2205, 2197])).
% 1.14/1.37 tff(2213,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2214,plain,
% 1.14/1.37 (~r(s(s(z)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2213, 2182, 1836, 2142, 2150])).
% 1.14/1.37 tff(2215,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[48, 45, 35, 2214, 2189])).
% 1.14/1.37 tff(2216,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2217,plain,
% 1.14/1.37 (~b(s(s(z)), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2216, 52, 53])).
% 1.14/1.37 tff(2218,plain,
% 1.14/1.37 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.14/1.37 inference(commutativity,[status(thm)],[])).
% 1.14/1.37 tff(2219,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 1.14/1.37 tff(2220,plain,
% 1.14/1.37 (s(s(s(z))) = s(s(z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2219, 2218])).
% 1.14/1.37 tff(2221,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[177, 2220])).
% 1.14/1.37 tff(2222,plain,((~(s(s(z)) = s(s(s(z))))) | (s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2223,plain,
% 1.14/1.37 (~(s(s(z)) = s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2222, 171])).
% 1.14/1.37 tff(2224,plain,
% 1.14/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2225,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(2226,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 1.14/1.37 tff(2227,plain,
% 1.14/1.37 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2226, 45])).
% 1.14/1.37 tff(2228,plain,
% 1.14/1.37 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2227, 2223])).
% 1.14/1.37 tff(2229,plain,
% 1.14/1.37 (r(s(s(z)), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2228, 2217])).
% 1.14/1.37 tff(2230,plain,
% 1.14/1.37 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[677, 273, 53, 649])).
% 1.14/1.37 tff(2231,plain,
% 1.14/1.37 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[698, 273, 53, 649, 492])).
% 1.14/1.37 tff(2232,plain,
% 1.14/1.37 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[186, 2231])).
% 1.14/1.37 tff(2233,plain,
% 1.14/1.37 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[617, 2232, 273, 53])).
% 1.14/1.37 tff(2234,plain,
% 1.14/1.37 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[386, 2233])).
% 1.14/1.37 tff(2235,plain,
% 1.14/1.37 (b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1928, 2234, 2230, 492])).
% 1.14/1.37 tff(2236,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[696, 233, 273, 649, 2235, 53])).
% 1.14/1.37 tff(2237,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(2238,plain,
% 1.14/1.37 (~b(z, s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2237, 492, 53, 649])).
% 1.14/1.37 tff(2239,plain,
% 1.14/1.37 (r(z, s(s(s(z))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[78, 2238])).
% 1.14/1.37 tff(2240,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.14/1.37 tff(2241,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(2242,plain,
% 1.14/1.37 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2243,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2242])).
% 1.14/1.38 tff(2244,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2243, 2241])).
% 1.14/1.38 tff(2245,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2246,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 1.14/1.38 tff(2247,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2246, 108, 493, 492, 2240, 97])).
% 1.14/1.38 tff(2248,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(2249,plain,
% 1.14/1.38 (~r(z, s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2248, 2239, 2229, 492])).
% 1.14/1.38 tff(2250,plain,
% 1.14/1.38 (b(z, s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[359, 2249])).
% 1.14/1.38 tff(2251,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2252,plain,
% 1.14/1.38 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2253,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2252])).
% 1.14/1.38 tff(2254,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2253, 2251])).
% 1.14/1.38 tff(2255,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2256,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 1.14/1.38 tff(2257,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2256, 233, 706, 649, 442, 53])).
% 1.14/1.38 tff(2258,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(2259,plain,
% 1.14/1.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2258, 2250, 53, 649])).
% 1.14/1.38 tff(2260,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[462, 2259])).
% 1.14/1.38 tff(2261,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2262,plain,
% 1.14/1.38 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2263,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2262])).
% 1.14/1.38 tff(2264,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2263, 2261])).
% 1.14/1.38 tff(2265,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2266,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 1.14/1.38 tff(2267,plain,
% 1.14/1.38 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2266, 233, 2250, 649, 53])).
% 1.14/1.38 tff(2268,plain,
% 1.14/1.38 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[440, 2267])).
% 1.14/1.38 tff(2269,plain,
% 1.14/1.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[688, 2268, 492, 2260])).
% 1.14/1.38 tff(2270,plain,
% 1.14/1.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[186, 2269])).
% 1.14/1.38 tff(2271,plain,
% 1.14/1.38 (~b(s(s(s(z))), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1906, 2270, 53, 2250])).
% 1.14/1.38 tff(2272,plain,
% 1.14/1.38 (r(s(s(s(z))), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[244, 2271])).
% 1.14/1.38 tff(2273,plain,
% 1.14/1.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2258, 706, 53, 649])).
% 1.14/1.38 tff(2274,plain,
% 1.14/1.38 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2266, 233, 706, 649, 53])).
% 1.14/1.38 tff(2275,plain,
% 1.14/1.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1928, 2274, 2273, 492])).
% 1.14/1.38 tff(2276,plain,
% 1.14/1.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[386, 2275])).
% 1.14/1.38 tff(2277,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[462, 2273])).
% 1.14/1.38 tff(2278,plain,
% 1.14/1.38 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[440, 2274])).
% 1.14/1.38 tff(2279,plain,
% 1.14/1.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[688, 2278, 492, 2277])).
% 1.14/1.38 tff(2280,plain,
% 1.14/1.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[186, 2279])).
% 1.14/1.38 tff(2281,plain,
% 1.14/1.38 (~b(z, s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[617, 2280, 2276, 53])).
% 1.14/1.38 tff(2282,plain,
% 1.14/1.38 (r(z, s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[78, 2281])).
% 1.14/1.38 tff(2283,plain,
% 1.14/1.38 (~r(s(z), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[477, 108, 2277, 2278, 52])).
% 1.14/1.38 tff(2284,plain,
% 1.14/1.38 (b(s(z), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[481, 45, 34, 2283])).
% 1.14/1.38 tff(2285,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2286,plain,
% 1.14/1.38 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2287,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2286])).
% 1.14/1.38 tff(2288,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2287, 2285])).
% 1.14/1.38 tff(2289,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2290,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.14/1.38 tff(2291,plain,
% 1.14/1.38 (~b(s(z), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2290, 233, 706, 649, 2284])).
% 1.14/1.38 tff(2292,plain,
% 1.14/1.38 (r(s(z), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[260, 2291])).
% 1.14/1.38 tff(2293,plain,
% 1.14/1.38 (~r(s(s(s(z))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[255, 2292, 2282, 247])).
% 1.14/1.38 tff(2294,plain,
% 1.14/1.38 (b(s(s(s(z))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1090, 2293])).
% 1.14/1.38 tff(2295,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2296,plain,
% 1.14/1.38 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2297,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2296])).
% 1.14/1.38 tff(2298,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2297, 2295])).
% 1.14/1.38 tff(2299,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2300,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 1.14/1.38 tff(2301,plain,
% 1.14/1.38 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2300, 233, 706, 649, 505, 504, 519])).
% 1.14/1.38 tff(2302,plain,
% 1.14/1.38 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[535, 45, 532, 2301])).
% 1.14/1.38 tff(2303,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2304,plain,
% 1.14/1.38 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2305,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[2304])).
% 1.14/1.38 tff(2306,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[2305, 2303])).
% 1.14/1.38 tff(2307,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(2308,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2307, 2306])).
% 1.14/1.38 tff(2309,plain,
% 1.14/1.38 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2308, 233, 505, 1072, 504])).
% 1.14/1.38 tff(2310,plain,
% 1.14/1.38 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[598, 2309])).
% 1.14/1.38 tff(2311,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2312,plain,
% 1.14/1.38 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(2313,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2312])).
% 1.14/1.39 tff(2314,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2313, 2311])).
% 1.14/1.39 tff(2315,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2316,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2315, 2314])).
% 1.14/1.39 tff(2317,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2316, 108, 492, 2240, 2310, 2302])).
% 1.14/1.39 tff(2318,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2319,plain,
% 1.14/1.39 (~b(s(s(s(s(s(z))))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2318, 2284, 2229, 492, 2294, 706, 649, 519])).
% 1.14/1.39 tff(2320,plain,
% 1.14/1.39 (r(s(s(s(s(s(z))))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[556, 2319, 91])).
% 1.14/1.39 tff(2321,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2322,plain,
% 1.14/1.39 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2323,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2322])).
% 1.14/1.39 tff(2324,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2323, 2321])).
% 1.14/1.39 tff(2325,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2326,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2325, 2324])).
% 1.14/1.39 tff(2327,plain,
% 1.14/1.39 (~b(z, s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2326, 233, 706, 649, 2284])).
% 1.14/1.39 tff(2328,plain,
% 1.14/1.39 (r(z, s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[128, 2327])).
% 1.14/1.39 tff(2329,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2330,plain,
% 1.14/1.39 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2331,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2330])).
% 1.14/1.39 tff(2332,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2331, 2329])).
% 1.14/1.39 tff(2333,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2334,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 1.14/1.39 tff(2335,plain,
% 1.14/1.39 (~r(s(s(s(s(s(z))))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2334, 108, 52, 2328, 2320])).
% 1.14/1.39 tff(2336,plain,
% 1.14/1.39 (b(s(s(s(s(s(z))))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[517, 45, 514, 2335])).
% 1.14/1.39 tff(2337,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.14/1.39 tff(2338,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2339,plain,
% 1.14/1.39 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2340,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2339])).
% 1.14/1.39 tff(2341,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2340, 2338])).
% 1.14/1.39 tff(2342,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2343,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2342, 2341])).
% 1.14/1.39 tff(2344,plain,
% 1.14/1.39 (~r(s(z), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2343, 108, 97, 247, 2337])).
% 1.14/1.39 tff(2345,plain,
% 1.14/1.39 (b(s(z), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[260, 2344])).
% 1.14/1.39 tff(2346,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2347,plain,
% 1.14/1.39 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2348,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2347])).
% 1.14/1.39 tff(2349,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2348, 2346])).
% 1.14/1.39 tff(2350,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2351,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 1.14/1.39 tff(2352,plain,
% 1.14/1.39 (~r(s(z), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2351, 108, 2240, 247, 2337])).
% 1.14/1.39 tff(2353,plain,
% 1.14/1.39 (b(s(z), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[481, 45, 34, 2352])).
% 1.14/1.39 tff(2354,plain,
% 1.14/1.39 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2355,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2354])).
% 1.14/1.39 tff(2356,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2355, 2285])).
% 1.14/1.39 tff(2357,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2358,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2357, 2356])).
% 1.14/1.39 tff(2359,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2358, 233, 706, 649, 2353, 2345])).
% 1.14/1.39 tff(2360,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2361,plain,
% 1.14/1.39 (~r(s(z), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2360, 2282, 2229, 247, 706, 649])).
% 1.14/1.39 tff(2362,plain,
% 1.14/1.39 (b(s(z), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[325, 2361])).
% 1.14/1.39 tff(2363,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2364,plain,
% 1.14/1.39 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2365,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2364])).
% 1.14/1.39 tff(2366,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2365, 2363])).
% 1.14/1.39 tff(2367,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2368,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 1.14/1.39 tff(2369,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2368, 233, 2276, 2280, 2362])).
% 1.14/1.39 tff(2370,plain,
% 1.14/1.39 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[200, 45, 2369])).
% 1.14/1.39 tff(2371,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2370, 96])).
% 1.14/1.39 tff(2372,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2373,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2374,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 1.14/1.39 tff(2375,plain,
% 1.14/1.39 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2374, 108, 52, 2320, 2371])).
% 1.14/1.39 tff(2376,plain,
% 1.14/1.39 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[579, 45, 576, 2375])).
% 1.14/1.39 tff(2377,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2378,plain,
% 1.14/1.39 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2379,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[2378])).
% 1.14/1.39 tff(2380,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[2379, 2377])).
% 1.14/1.39 tff(2381,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(2382,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[2381, 2380])).
% 1.14/1.39 tff(2383,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2382, 233, 706, 53, 2376, 2336])).
% 1.14/1.39 tff(2384,plain,((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2385,plain,
% 1.14/1.39 (~b(s(s(z)), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2384, 2272, 52, 492, 649, 2250, 53])).
% 1.14/1.39 tff(2386,plain,
% 1.14/1.39 (~r(s(s(z)), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[469, 108, 2260, 2268, 52])).
% 1.14/1.39 tff(2387,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[48, 45, 35, 2386, 2385])).
% 1.14/1.39 tff(2388,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(2389,plain,
% 1.14/1.39 (~r(s(s(s(z))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2388, 649, 52, 53])).
% 1.14/1.39 tff(2390,plain,
% 1.14/1.39 (b(s(s(s(z))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[340, 2389])).
% 1.14/1.39 tff(2391,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2392,plain,
% 1.14/1.39 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2393,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2392])).
% 1.14/1.40 tff(2394,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.14/1.40 inference(transitivity,[status(thm)],[2393, 2391])).
% 1.14/1.40 tff(2395,plain,
% 1.14/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.40 inference(quant_inst,[status(thm)],[])).
% 1.14/1.40 tff(2396,plain,
% 1.14/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 1.14/1.40 tff(2397,plain,
% 1.14/1.40 ($false),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[2396, 233, 284, 649, 442, 204])).
% 1.14/1.40 tff(2398,plain,((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.40 tff(2399,plain,
% 1.14/1.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[2398, 204, 649, 2390])).
% 1.14/1.40 tff(2400,plain,
% 1.14/1.40 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[462, 2399])).
% 1.14/1.40 tff(2401,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.14/1.40 tff(2402,plain,
% 1.14/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(2403,plain,
% 1.14/1.40 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(2404,plain,
% 1.14/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[2403])).
% 1.14/1.40 tff(2405,plain,
% 1.14/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.40 inference(transitivity,[status(thm)],[2404, 2402])).
% 1.14/1.40 tff(2406,plain,
% 1.14/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2407,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 1.24/1.40 tff(2408,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2407, 108, 2240, 680, 52, 2401])).
% 1.24/1.40 tff(2409,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2410,plain,
% 1.24/1.40 (~r(s(z), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2409, 2400, 2229, 52])).
% 1.24/1.40 tff(2411,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.24/1.40 tff(2412,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 1.24/1.40 tff(2413,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[481, 45, 34, 2412, 2411])).
% 1.24/1.40 tff(2414,plain,(r(s(z), s(s(z))) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2415,plain,
% 1.24/1.40 (b(s(z), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2414, 2410])).
% 1.24/1.40 tff(2416,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2417,plain,
% 1.24/1.40 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2418,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2417])).
% 1.24/1.40 tff(2419,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2418, 2416])).
% 1.24/1.40 tff(2420,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2421,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 1.24/1.40 tff(2422,plain,
% 1.24/1.40 (~b(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2421, 233, 2390, 649, 2415])).
% 1.24/1.40 tff(2423,plain,
% 1.24/1.40 (r(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1090, 2422])).
% 1.24/1.40 tff(2424,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2425,plain,
% 1.24/1.40 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2426,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2425])).
% 1.24/1.40 tff(2427,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2426, 2424])).
% 1.24/1.40 tff(2428,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2429,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 1.24/1.40 tff(2430,plain,
% 1.24/1.40 (~b(s(z), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2429, 233, 2390, 649, 2415])).
% 1.24/1.40 tff(2431,plain,
% 1.24/1.40 (r(s(z), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[325, 2430])).
% 1.24/1.40 tff(2432,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[617, 273, 204, 53])).
% 1.24/1.40 tff(2433,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[334, 273, 52, 284, 92, 247])).
% 1.24/1.40 tff(2434,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[386, 2433, 2432])).
% 1.24/1.40 tff(2435,plain,((~b(z, s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2436,plain,
% 1.24/1.40 (~b(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2435, 247, 2390, 2423, 52, 204, 53])).
% 1.24/1.40 tff(2437,plain,
% 1.24/1.40 (r(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[78, 2436])).
% 1.24/1.40 tff(2438,plain,
% 1.24/1.40 (~b(z, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2360, 2437, 2229, 2431, 247, 649])).
% 1.24/1.40 tff(2439,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2440,plain,
% 1.24/1.40 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2441,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2440])).
% 1.24/1.40 tff(2442,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2441, 2439])).
% 1.24/1.40 tff(2443,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2444,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 1.24/1.40 tff(2445,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2444, 108, 493, 2240, 97, 92])).
% 1.24/1.40 tff(2446,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2447,plain,
% 1.24/1.40 (~r(z, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2446, 2437, 2229, 2423])).
% 1.24/1.40 tff(2448,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[359, 2447, 2438])).
% 1.24/1.40 tff(2449,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2450,plain,
% 1.24/1.40 (~r(s(s(s(z))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2449, 204, 52, 649, 53])).
% 1.24/1.40 tff(2451,plain,
% 1.24/1.40 (b(s(s(s(z))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[244, 2450])).
% 1.24/1.40 tff(2452,plain,
% 1.24/1.40 (~b(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[281, 2451, 53, 204])).
% 1.24/1.40 tff(2453,plain,
% 1.24/1.40 (r(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[78, 2452])).
% 1.24/1.40 tff(2454,plain,
% 1.24/1.40 (~b(z, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1906, 2451, 53, 204])).
% 1.24/1.40 tff(2455,plain,
% 1.24/1.40 (r(z, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[359, 2454])).
% 1.24/1.40 tff(2456,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2446, 2455, 2453, 2229, 2423])).
% 1.24/1.40 tff(2457,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2458,plain,
% 1.24/1.40 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2457, 649, 52, 53])).
% 1.24/1.40 tff(2459,plain,
% 1.24/1.40 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[186, 2458])).
% 1.24/1.40 tff(2460,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2461,plain,
% 1.24/1.40 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2462,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2461])).
% 1.24/1.40 tff(2463,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2462, 2460])).
% 1.24/1.40 tff(2464,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2465,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2464, 2463])).
% 1.24/1.40 tff(2466,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2465, 108, 2240, 2277, 2278, 81])).
% 1.24/1.40 tff(2467,plain,((~b(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2468,plain,
% 1.24/1.40 (~b(z, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2467, 2459, 2229, 649, 53])).
% 1.24/1.40 tff(2469,plain,
% 1.24/1.40 (r(z, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[359, 2468])).
% 1.24/1.40 tff(2470,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2471,plain,
% 1.24/1.40 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2472,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2471])).
% 1.24/1.40 tff(2473,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2472, 2470])).
% 1.24/1.40 tff(2474,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2475,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2474, 2473])).
% 1.24/1.40 tff(2476,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2475, 108, 493, 2240, 97, 81])).
% 1.24/1.40 tff(2477,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(2478,plain,
% 1.24/1.40 (~r(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2477, 2469, 2229, 2459])).
% 1.24/1.40 tff(2479,plain,
% 1.24/1.40 (b(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[78, 2478])).
% 1.24/1.40 tff(2480,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[677, 2479, 53, 649])).
% 1.24/1.40 tff(2481,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[462, 2480])).
% 1.24/1.40 tff(2482,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2483,plain,
% 1.24/1.40 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(2484,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[2483])).
% 1.24/1.40 tff(2485,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[2484, 2482])).
% 1.24/1.40 tff(2486,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(2487,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2486, 2485])).
% 1.24/1.40 tff(2488,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2487, 108, 130, 2240, 680, 81])).
% 1.24/1.41 tff(2489,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2490,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2489, 2481, 2229, 2459])).
% 1.24/1.41 tff(2491,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[386, 2490])).
% 1.24/1.41 tff(2492,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1832, 233, 2491, 2390, 2479, 53])).
% 1.24/1.41 tff(2493,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2494,plain,
% 1.24/1.41 (~b(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2493, 52, 53])).
% 1.24/1.41 tff(2495,plain,
% 1.24/1.41 (r(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[374, 2494])).
% 1.24/1.41 tff(2496,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2497,plain,
% 1.24/1.41 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2498,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2497])).
% 1.24/1.41 tff(2499,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2498, 2496])).
% 1.24/1.41 tff(2500,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2501,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 1.24/1.41 tff(2502,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2501, 108, 130, 492, 2240, 491])).
% 1.24/1.41 tff(2503,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2504,plain,
% 1.24/1.41 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2503, 130, 2240, 492])).
% 1.24/1.41 tff(2505,plain,
% 1.24/1.41 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[440, 2504])).
% 1.24/1.41 tff(2506,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2507,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2508,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 1.24/1.41 tff(2509,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2508, 108, 130, 701, 492, 680])).
% 1.24/1.41 tff(2510,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2511,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2510, 130, 701, 492])).
% 1.24/1.41 tff(2512,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[462, 2511])).
% 1.24/1.41 tff(2513,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2514,plain,
% 1.24/1.41 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2515,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2514])).
% 1.24/1.41 tff(2516,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2515, 2513])).
% 1.24/1.41 tff(2517,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2518,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 1.24/1.41 tff(2519,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2518, 233, 706, 2512, 2505, 53])).
% 1.24/1.41 tff(2520,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2521,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2520, 492, 53, 2495, 706, 2229])).
% 1.24/1.41 tff(2522,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[386, 2521])).
% 1.24/1.41 tff(2523,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2524,plain,
% 1.24/1.41 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2525,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2524])).
% 1.24/1.41 tff(2526,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2525, 2523])).
% 1.24/1.41 tff(2527,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2528,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 1.24/1.41 tff(2529,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2528, 233, 389, 273, 53, 1072])).
% 1.24/1.41 tff(2530,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2531,plain,
% 1.24/1.41 (~b(s(s(s(z))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2530, 2522, 53, 273])).
% 1.24/1.41 tff(2532,plain,
% 1.24/1.41 (r(s(s(s(z))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1090, 2531])).
% 1.24/1.41 tff(2533,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2534,plain,
% 1.24/1.41 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2535,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2534])).
% 1.24/1.41 tff(2536,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2535, 2533])).
% 1.24/1.41 tff(2537,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2538,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.24/1.41 tff(2539,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2538, 108, 2240, 92, 2051, 52])).
% 1.24/1.41 tff(2540,plain,((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2541,plain,
% 1.24/1.41 (~r(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2540, 2532, 2229, 52])).
% 1.24/1.41 tff(2542,plain,
% 1.24/1.41 (b(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[48, 45, 35, 2541])).
% 1.24/1.41 tff(2543,plain,
% 1.24/1.41 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[617, 2522, 273, 53])).
% 1.24/1.41 tff(2544,plain,
% 1.24/1.41 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[186, 2543])).
% 1.24/1.41 tff(2545,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2546,plain,
% 1.24/1.41 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2547,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2546])).
% 1.24/1.41 tff(2548,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2547, 2545])).
% 1.24/1.41 tff(2549,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2550,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 1.24/1.41 tff(2551,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2550, 108, 701, 492, 680, 81])).
% 1.24/1.41 tff(2552,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2553,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2552, 492, 2495, 2544])).
% 1.24/1.41 tff(2554,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[462, 2553])).
% 1.24/1.41 tff(2555,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2556,plain,
% 1.24/1.41 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2557,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2556])).
% 1.24/1.41 tff(2558,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2557, 2555])).
% 1.24/1.41 tff(2559,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2560,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 1.24/1.41 tff(2561,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2560, 233, 706, 2554, 53, 2542])).
% 1.24/1.41 tff(2562,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2563,plain,
% 1.24/1.41 (~r(s(s(s(z))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2562, 273, 53, 52, 706])).
% 1.24/1.41 tff(2564,plain,
% 1.24/1.41 (b(s(s(s(z))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[340, 2563])).
% 1.24/1.41 tff(2565,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2566,plain,
% 1.24/1.41 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(2567,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[2566])).
% 1.24/1.41 tff(2568,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[2567, 2565])).
% 1.24/1.41 tff(2569,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(2570,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 1.24/1.41 tff(2571,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2570, 233, 284, 273, 706, 424])).
% 1.24/1.41 tff(2572,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(2573,plain,
% 1.24/1.41 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2572, 2564, 706, 273])).
% 1.24/1.41 tff(2574,plain,
% 1.24/1.41 (r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[440, 2573])).
% 1.24/1.41 tff(2575,plain,
% 1.24/1.42 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[617, 204, 273, 53])).
% 1.24/1.42 tff(2576,plain,
% 1.24/1.42 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[386, 2575])).
% 1.24/1.42 tff(2577,plain,
% 1.24/1.42 (~b(s(s(s(z))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1906, 204, 53, 706])).
% 1.24/1.42 tff(2578,plain,
% 1.24/1.42 (r(s(s(s(z))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[244, 2577])).
% 1.24/1.42 tff(2579,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2580,plain,
% 1.24/1.42 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2581,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2580])).
% 1.24/1.42 tff(2582,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2581, 2579])).
% 1.24/1.42 tff(2583,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2584,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2583, 2582])).
% 1.24/1.42 tff(2585,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2584, 108, 130, 2240, 491, 247])).
% 1.24/1.42 tff(2586,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2587,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2586, 2578, 2576, 2240, 491])).
% 1.24/1.42 tff(2588,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2589,plain,
% 1.24/1.42 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2588, 2574, 2229, 53, 706, 273])).
% 1.24/1.42 tff(2590,plain,
% 1.24/1.42 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[186, 2589])).
% 1.24/1.42 tff(2591,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2592,plain,
% 1.24/1.42 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2593,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2592])).
% 1.24/1.42 tff(2594,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2593, 2591])).
% 1.24/1.42 tff(2595,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2596,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 1.24/1.42 tff(2597,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2596, 108, 130, 2240, 491, 81])).
% 1.24/1.42 tff(2598,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2599,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2598, 2590, 2229, 2574])).
% 1.24/1.42 tff(2600,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[386, 2599])).
% 1.24/1.42 tff(2601,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1832, 233, 2600, 2564, 273, 53])).
% 1.24/1.42 tff(2602,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2603,plain,
% 1.24/1.42 (~b(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2602, 706, 53, 52])).
% 1.24/1.42 tff(2604,plain,
% 1.24/1.42 (r(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[78, 2603])).
% 1.24/1.42 tff(2605,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2606,plain,
% 1.24/1.42 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2607,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2606])).
% 1.24/1.42 tff(2608,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2607, 2605])).
% 1.24/1.42 tff(2609,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2610,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 1.24/1.42 tff(2611,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2610, 108, 701, 2240, 97, 81])).
% 1.24/1.42 tff(2612,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2613,plain,
% 1.24/1.42 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2612, 2604, 2229, 2495])).
% 1.24/1.42 tff(2614,plain,
% 1.24/1.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[186, 2613])).
% 1.24/1.42 tff(2615,plain,
% 1.24/1.42 (~b(s(s(s(z))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1906, 2614, 53, 706])).
% 1.24/1.42 tff(2616,plain,
% 1.24/1.42 (r(s(s(s(z))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[244, 2615])).
% 1.24/1.42 tff(2617,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2618,plain,
% 1.24/1.42 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2619,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2618])).
% 1.24/1.42 tff(2620,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2619, 2617])).
% 1.24/1.42 tff(2621,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2622,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2621, 2620])).
% 1.24/1.42 tff(2623,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2622, 108, 2495, 2229, 2604, 2616])).
% 1.24/1.42 tff(2624,plain,((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2625,plain,
% 1.24/1.42 (~b(z, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2624, 52, 53])).
% 1.24/1.42 tff(2626,plain,
% 1.24/1.42 (r(z, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[359, 2625])).
% 1.24/1.42 tff(2627,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2628,plain,
% 1.24/1.42 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2629,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2628])).
% 1.24/1.42 tff(2630,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2629, 2627])).
% 1.24/1.42 tff(2631,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2632,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2631, 2630])).
% 1.24/1.42 tff(2633,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2632, 108, 701, 493, 2240, 247])).
% 1.24/1.42 tff(2634,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2635,plain,
% 1.24/1.42 (~r(s(s(s(z))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2634, 2495, 2626, 2229])).
% 1.24/1.42 tff(2636,plain,
% 1.24/1.42 (b(s(s(s(z))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[244, 2635])).
% 1.24/1.42 tff(2637,plain,
% 1.24/1.42 (~b(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[281, 204, 53, 2636])).
% 1.24/1.42 tff(2638,plain,
% 1.24/1.42 (r(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[78, 2637])).
% 1.24/1.42 tff(2639,plain,
% 1.24/1.42 (~r(s(s(s(z))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2248, 2638, 2229, 2626])).
% 1.24/1.42 tff(2640,plain,
% 1.24/1.42 (b(s(s(s(z))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[340, 2639])).
% 1.24/1.42 tff(2641,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2642,plain,
% 1.24/1.42 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2643,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2642])).
% 1.24/1.42 tff(2644,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2643, 2641])).
% 1.24/1.42 tff(2645,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2646,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.24/1.42 tff(2647,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2646, 108, 701, 2240, 97, 92])).
% 1.24/1.42 tff(2648,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2649,plain,
% 1.24/1.42 (~r(s(s(s(z))), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2648, 2638, 2229, 2495])).
% 1.24/1.42 tff(2650,plain,
% 1.24/1.42 (b(s(s(s(z))), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1090, 2649])).
% 1.24/1.42 tff(2651,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2652,plain,
% 1.24/1.42 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2653,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2652])).
% 1.24/1.42 tff(2654,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[2653, 2651])).
% 1.24/1.42 tff(2655,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(2656,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[2655, 2654])).
% 1.24/1.42 tff(2657,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2656, 233, 284, 424, 53, 204])).
% 1.24/1.42 tff(2658,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(2659,plain,
% 1.24/1.42 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2658, 2640, 53, 204])).
% 1.24/1.42 tff(2660,plain,
% 1.24/1.42 (r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[440, 2659])).
% 1.24/1.42 tff(2661,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1894, 2660, 52, 2650, 2640])).
% 1.24/1.42 tff(2662,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[386, 2661])).
% 1.24/1.42 tff(2663,plain,
% 1.24/1.42 (~b(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[397, 2662, 53, 2636])).
% 1.24/1.42 tff(2664,plain,
% 1.24/1.42 (r(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[128, 2663])).
% 1.24/1.42 tff(2665,plain,
% 1.24/1.42 (~r(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2126, 2664, 2495, 52])).
% 1.24/1.42 tff(2666,plain,
% 1.24/1.42 (b(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[50, 2665])).
% 1.24/1.42 tff(2667,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2668,plain,
% 1.24/1.42 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(2669,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[2668])).
% 1.24/1.42 tff(2670,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2669, 2667])).
% 1.24/1.43 tff(2671,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2672,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2671, 2670])).
% 1.24/1.43 tff(2673,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2672, 233, 389, 284, 442, 519])).
% 1.24/1.43 tff(2674,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2675,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2674, 2666, 2640, 2662])).
% 1.24/1.43 tff(2676,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[462, 2675])).
% 1.24/1.43 tff(2677,plain,
% 1.24/1.43 (~r(s(z), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2409, 2676, 2229, 52])).
% 1.24/1.43 tff(2678,plain,
% 1.24/1.43 (b(s(z), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2414, 2677])).
% 1.24/1.43 tff(2679,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1892, 233, 2640, 2678, 2650, 2666])).
% 1.24/1.43 tff(2680,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2681,plain,
% 1.24/1.43 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2680, 52, 53])).
% 1.24/1.43 tff(2682,plain,
% 1.24/1.43 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[186, 2681])).
% 1.24/1.43 tff(2683,plain,
% 1.24/1.43 (~r(z, s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2612, 2682, 2229, 2495])).
% 1.24/1.43 tff(2684,plain,
% 1.24/1.43 (b(z, s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[78, 2683])).
% 1.24/1.43 tff(2685,plain,
% 1.24/1.43 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2686,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2685])).
% 1.24/1.43 tff(2687,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2686, 620])).
% 1.24/1.43 tff(2688,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2689,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 1.24/1.43 tff(2690,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2689, 233, 389, 273, 272, 53])).
% 1.24/1.43 tff(2691,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2692,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2691, 2684, 2636, 53])).
% 1.24/1.43 tff(2693,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[386, 2692])).
% 1.24/1.43 tff(2694,plain,
% 1.24/1.43 (~r(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1971, 108, 2693, 2682, 52])).
% 1.24/1.43 tff(2695,plain,
% 1.24/1.43 (b(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[325, 2694])).
% 1.24/1.43 tff(2696,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2697,plain,
% 1.24/1.43 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2698,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2697])).
% 1.24/1.43 tff(2699,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2698, 2696])).
% 1.24/1.43 tff(2700,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2701,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2700, 2699])).
% 1.24/1.43 tff(2702,plain,
% 1.24/1.43 (~b(s(s(s(s(s(z))))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2701, 233, 273, 272, 1547])).
% 1.24/1.43 tff(2703,plain,
% 1.24/1.43 (r(s(s(s(s(s(z))))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[517, 45, 514, 2702])).
% 1.24/1.43 tff(2704,assumption,(~(s(s(s(s(s(z))))) = s(z))), introduced(assumption)).
% 1.24/1.43 tff(2705,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2706,plain,
% 1.24/1.43 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2707,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2706])).
% 1.24/1.43 tff(2708,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2707, 2705])).
% 1.24/1.43 tff(2709,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2710,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 1.24/1.43 tff(2711,plain,
% 1.24/1.43 (~b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2710, 233, 272, 1547, 285])).
% 1.24/1.43 tff(2712,plain,
% 1.24/1.43 (r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[556, 2711, 2704])).
% 1.24/1.43 tff(2713,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2714,plain,
% 1.24/1.43 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2715,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2714])).
% 1.24/1.43 tff(2716,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2715, 2713])).
% 1.24/1.43 tff(2717,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2718,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 1.24/1.43 tff(2719,plain,
% 1.24/1.43 (~b(z, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2718, 233, 273, 272, 285])).
% 1.24/1.43 tff(2720,plain,
% 1.24/1.43 (r(z, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[128, 2719])).
% 1.24/1.43 tff(2721,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2334, 108, 52, 2720, 2712, 2703])).
% 1.24/1.43 tff(2722,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2723,plain,
% 1.24/1.43 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2722, 2695, 52, 2684, 2636, 91])).
% 1.24/1.43 tff(2724,plain,
% 1.24/1.43 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[598, 2723])).
% 1.24/1.43 tff(2725,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2726,plain,
% 1.24/1.43 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2727,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2726])).
% 1.24/1.43 tff(2728,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2727, 2725])).
% 1.24/1.43 tff(2729,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2730,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2729, 2728])).
% 1.24/1.43 tff(2731,plain,
% 1.24/1.43 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2730, 108, 2229, 2682, 2724])).
% 1.24/1.43 tff(2732,plain,
% 1.24/1.43 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[535, 45, 532, 2731])).
% 1.24/1.43 tff(2733,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2734,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2735,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 1.24/1.43 tff(2736,plain,
% 1.24/1.43 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2735, 108, 2693, 2682, 2724])).
% 1.24/1.43 tff(2737,plain,
% 1.24/1.43 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[579, 45, 576, 2736])).
% 1.24/1.43 tff(2738,plain,
% 1.24/1.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2598, 2693, 2229, 2682])).
% 1.24/1.43 tff(2739,plain,
% 1.24/1.43 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[440, 2738])).
% 1.24/1.43 tff(2740,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2489, 2693, 2229, 2682])).
% 1.24/1.43 tff(2741,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[462, 2740])).
% 1.24/1.43 tff(2742,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2743,plain,
% 1.24/1.43 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2744,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[2743])).
% 1.24/1.43 tff(2745,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[2744, 2742])).
% 1.24/1.43 tff(2746,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(2747,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 1.24/1.43 tff(2748,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2747, 233, 2741, 2739, 2737, 2732])).
% 1.24/1.43 tff(2749,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(2750,plain,
% 1.24/1.43 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2749, 53])).
% 1.24/1.43 tff(2751,plain,
% 1.24/1.43 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1122, 2750])).
% 1.24/1.43 tff(2752,plain,
% 1.24/1.43 (~r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[2010, 108, 130, 97, 81])).
% 1.24/1.43 tff(2753,plain,
% 1.24/1.43 (b(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[222, 2752])).
% 1.24/1.43 tff(2754,plain,
% 1.24/1.43 (~r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1949, 97, 492, 130])).
% 1.24/1.43 tff(2755,plain,
% 1.24/1.43 (b(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[222, 2754])).
% 1.24/1.43 tff(2756,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(2757,plain,
% 1.24/1.43 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2758,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2757])).
% 1.24/1.44 tff(2759,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2758, 2756])).
% 1.24/1.44 tff(2760,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2761,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 1.24/1.44 tff(2762,plain,
% 1.24/1.44 (~b(s(z), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2761, 233, 2755, 53, 2751])).
% 1.24/1.44 tff(2763,plain,
% 1.24/1.44 (r(s(z), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[260, 2762])).
% 1.24/1.44 tff(2764,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2765,plain,
% 1.24/1.44 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2766,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2765])).
% 1.24/1.44 tff(2767,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2766, 2764])).
% 1.24/1.44 tff(2768,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2769,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2768, 2767])).
% 1.24/1.44 tff(2770,plain,
% 1.24/1.44 (~b(z, s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2769, 233, 2755, 53, 2751])).
% 1.24/1.44 tff(2771,plain,
% 1.24/1.44 (r(z, s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[128, 2770])).
% 1.24/1.44 tff(2772,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2773,plain,
% 1.24/1.44 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2774,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2773])).
% 1.24/1.44 tff(2775,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2774, 2772])).
% 1.24/1.44 tff(2776,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2777,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2776, 2775])).
% 1.24/1.44 tff(2778,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2777, 108, 97, 92, 98, 246])).
% 1.24/1.44 tff(2779,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2780,plain,
% 1.24/1.44 (~r(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2779, 97, 2771, 2763])).
% 1.24/1.44 tff(2781,plain,
% 1.24/1.44 (b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1090, 2780])).
% 1.24/1.44 tff(2782,plain,
% 1.24/1.44 (~b(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2108, 2781, 80, 53, 492, 97, 81])).
% 1.24/1.44 tff(2783,plain,
% 1.24/1.44 (r(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[374, 2782])).
% 1.24/1.44 tff(2784,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2785,plain,
% 1.24/1.44 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2786,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2785])).
% 1.24/1.44 tff(2787,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2786, 2784])).
% 1.24/1.44 tff(2788,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2789,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 1.24/1.44 tff(2790,plain,
% 1.24/1.44 (~b(s(z), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2789, 233, 80, 1072, 285])).
% 1.24/1.44 tff(2791,plain,
% 1.24/1.44 (r(s(z), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2414, 2790])).
% 1.24/1.44 tff(2792,plain,
% 1.24/1.44 (~b(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1979, 233, 80, 1072, 285])).
% 1.24/1.44 tff(2793,plain,
% 1.24/1.44 (r(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[50, 2792])).
% 1.24/1.44 tff(2794,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2795,plain,
% 1.24/1.44 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2796,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2795])).
% 1.24/1.44 tff(2797,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2796, 2794])).
% 1.24/1.44 tff(2798,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2799,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 1.24/1.44 tff(2800,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2799, 108, 701, 2793, 98, 2791])).
% 1.24/1.44 tff(2801,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2802,plain,
% 1.24/1.44 (~b(s(z), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2801, 2783, 2771, 80, 2781])).
% 1.24/1.44 tff(2803,plain,
% 1.24/1.44 (r(s(z), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[325, 2802])).
% 1.24/1.44 tff(2804,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2805,plain,
% 1.24/1.44 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2806,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2805])).
% 1.24/1.44 tff(2807,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2806, 2804])).
% 1.24/1.44 tff(2808,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2809,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 1.24/1.44 tff(2810,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2809, 108, 492, 97, 2803, 2763])).
% 1.24/1.44 tff(2811,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2812,plain,
% 1.24/1.44 (~r(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2811, 492, 80, 53, 81, 130])).
% 1.24/1.44 tff(2813,plain,
% 1.24/1.44 (b(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[78, 2812])).
% 1.24/1.44 tff(2814,plain,
% 1.24/1.44 (~b(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2237, 2813, 53, 492])).
% 1.24/1.44 tff(2815,plain,
% 1.24/1.44 (r(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[374, 2814])).
% 1.24/1.44 tff(2816,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2552, 2815, 492, 81])).
% 1.24/1.44 tff(2817,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[462, 2816])).
% 1.24/1.44 tff(2818,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2819,plain,
% 1.24/1.44 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2820,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2819])).
% 1.24/1.44 tff(2821,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2820, 2818])).
% 1.24/1.44 tff(2822,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2823,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 1.24/1.44 tff(2824,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2823, 233, 80, 273, 442, 53, 2751, 402])).
% 1.24/1.44 tff(2825,plain,((~b(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2826,plain,
% 1.24/1.44 (~b(s(z), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2825, 2813, 80, 2817, 53])).
% 1.24/1.44 tff(2827,plain,
% 1.24/1.44 (r(s(z), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[260, 2826])).
% 1.24/1.44 tff(2828,plain,
% 1.24/1.44 (~b(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2237, 273, 53, 492])).
% 1.24/1.44 tff(2829,plain,
% 1.24/1.44 (r(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[374, 2828])).
% 1.24/1.44 tff(2830,plain,
% 1.24/1.44 (~r(z, elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1251, 247, 492, 2829])).
% 1.24/1.44 tff(2831,plain,
% 1.24/1.44 (~r(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[703, 247, 492, 2829])).
% 1.24/1.44 tff(2832,plain,
% 1.24/1.44 (b(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[359, 2831])).
% 1.24/1.44 tff(2833,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2156, 233, 80, 273, 706, 1072])).
% 1.24/1.44 tff(2834,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2835,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2834, 2832, 273, 80])).
% 1.24/1.44 tff(2836,plain,
% 1.24/1.44 (r(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1090, 2835])).
% 1.24/1.44 tff(2837,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.44 tff(2838,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2839,plain,
% 1.24/1.44 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(2840,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[2839])).
% 1.24/1.44 tff(2841,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[2840, 2838])).
% 1.24/1.44 tff(2842,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(2843,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[2842, 2841])).
% 1.24/1.44 tff(2844,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2843, 233, 80, 273, 706, 2837])).
% 1.24/1.44 tff(2845,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(2846,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2845, 2832, 273, 80])).
% 1.24/1.45 tff(2847,plain,
% 1.24/1.45 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[759, 2846])).
% 1.24/1.45 tff(2848,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.24/1.45 tff(2849,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.45 tff(2850,plain,
% 1.24/1.45 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.24/1.45 inference(commutativity,[status(thm)],[])).
% 1.24/1.45 tff(2851,plain,
% 1.24/1.45 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[2850])).
% 1.24/1.45 tff(2852,plain,
% 1.24/1.45 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2851])).
% 1.24/1.45 tff(2853,plain,
% 1.24/1.45 (~(z = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[514, 2852])).
% 1.24/1.45 tff(2854,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(2855,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2856,plain,
% 1.24/1.45 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2857,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2856])).
% 1.24/1.45 tff(2858,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2857, 2855])).
% 1.24/1.45 tff(2859,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2860,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2859, 2858])).
% 1.24/1.45 tff(2861,plain,
% 1.24/1.45 (~b(z, s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2860, 233, 2854, 388, 504])).
% 1.24/1.45 tff(2862,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2863,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2864,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2863, 2862])).
% 1.24/1.45 tff(2865,plain,
% 1.24/1.45 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2864, 45, 2861])).
% 1.24/1.45 tff(2866,plain,
% 1.24/1.45 (r(z, s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2865, 2853])).
% 1.24/1.45 tff(2867,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2868,plain,
% 1.24/1.45 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2869,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2868])).
% 1.24/1.45 tff(2870,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2869, 2867])).
% 1.24/1.45 tff(2871,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2872,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 1.24/1.45 tff(2873,plain,
% 1.24/1.45 (~b(s(s(s(s(s(z))))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2872, 233, 2854, 388, 504])).
% 1.24/1.45 tff(2874,plain,
% 1.24/1.45 (r(s(s(s(s(s(z))))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[517, 45, 514, 2873])).
% 1.24/1.45 tff(2875,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2876,plain,
% 1.24/1.45 (((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2877,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2876])).
% 1.24/1.45 tff(2878,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2877, 2875])).
% 1.24/1.45 tff(2879,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2880,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 1.24/1.45 tff(2881,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2880, 108, 247, 2849, 2874, 2866])).
% 1.24/1.45 tff(2882,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2883,plain,
% 1.24/1.45 (~b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2882, 388, 2849, 2751, 247])).
% 1.24/1.45 tff(2884,plain,
% 1.24/1.45 (r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[556, 2883, 91])).
% 1.24/1.45 tff(2885,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2886,plain,
% 1.24/1.45 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2887,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2886])).
% 1.24/1.45 tff(2888,plain,
% 1.24/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2887, 2885])).
% 1.24/1.45 tff(2889,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2890,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2889, 2888])).
% 1.24/1.45 tff(2891,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2890, 108, 92, 2849, 246, 747])).
% 1.24/1.45 tff(2892,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2893,plain,
% 1.24/1.45 (~r(s(z), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2892, 2884, 2849, 92])).
% 1.24/1.45 tff(2894,plain,
% 1.24/1.45 (b(s(z), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[260, 2893])).
% 1.24/1.45 tff(2895,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2896,plain,
% 1.24/1.45 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2897,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2896])).
% 1.24/1.45 tff(2898,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2897, 2895])).
% 1.24/1.45 tff(2899,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2900,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2899, 2898])).
% 1.24/1.45 tff(2901,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2900, 233, 921, 53, 2751, 402])).
% 1.24/1.45 tff(2902,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2903,plain,
% 1.24/1.45 (~b(z, elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2902, 2894, 53])).
% 1.24/1.45 tff(2904,plain,
% 1.24/1.45 (z = elem!1),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[934, 2903, 2848])).
% 1.24/1.45 tff(2905,plain,
% 1.24/1.45 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1726])).
% 1.24/1.45 tff(2906,plain,
% 1.24/1.45 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[2905])).
% 1.24/1.45 tff(2907,plain,
% 1.24/1.45 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1724, 2906])).
% 1.24/1.45 tff(2908,plain,
% 1.24/1.45 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[2907])).
% 1.24/1.45 tff(2909,plain,
% 1.24/1.45 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2854, 2908])).
% 1.24/1.45 tff(2910,assumption,(~b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.45 tff(2911,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2910, 2909])).
% 1.24/1.45 tff(2912,plain,(b(s(elem!1), s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2913,plain,
% 1.24/1.45 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2912, 2904, 2751])).
% 1.24/1.45 tff(2914,plain,
% 1.24/1.45 (s(z) = s(elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2904])).
% 1.24/1.45 tff(2915,plain,
% 1.24/1.45 (s(s(z)) = s(s(elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2914])).
% 1.24/1.45 tff(2916,plain,
% 1.24/1.45 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2915])).
% 1.24/1.45 tff(2917,plain,
% 1.24/1.45 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2916])).
% 1.24/1.45 tff(2918,plain,
% 1.24/1.45 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[2917])).
% 1.24/1.45 tff(2919,plain,
% 1.24/1.45 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2918])).
% 1.24/1.45 tff(2920,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.45 inference(symmetry,[status(thm)],[2919])).
% 1.24/1.45 tff(2921,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2904])).
% 1.24/1.45 tff(2922,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[53, 2921])).
% 1.24/1.45 tff(2923,plain,
% 1.24/1.45 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2922, 2920])).
% 1.24/1.45 tff(2924,plain,
% 1.24/1.45 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2914])).
% 1.24/1.45 tff(2925,plain,
% 1.24/1.45 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2904])).
% 1.24/1.45 tff(2926,plain,
% 1.24/1.45 (b(s(z), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2894, 2925])).
% 1.24/1.45 tff(2927,plain,
% 1.24/1.45 (b(s(elem!1), elem!1)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2926, 2924])).
% 1.24/1.45 tff(2928,plain,
% 1.24/1.45 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2914])).
% 1.24/1.45 tff(2929,plain,
% 1.24/1.45 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2904])).
% 1.24/1.45 tff(2930,plain,
% 1.24/1.45 (b(elem!1, s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[388, 2929])).
% 1.24/1.45 tff(2931,plain,
% 1.24/1.45 (b(elem!1, s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2930, 2928])).
% 1.24/1.45 tff(2932,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2933,plain,
% 1.24/1.45 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(2934,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2933])).
% 1.24/1.45 tff(2935,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[2934, 2932])).
% 1.24/1.45 tff(2936,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(2937,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 1.24/1.45 tff(2938,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2937, 233, 2931, 2927, 2923, 2913])).
% 1.24/1.45 tff(2939,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | r(z, elem!1) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2940,plain,
% 1.24/1.45 (~b(z, s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2939, 2830, 53, 2847, 2836, 247])).
% 1.24/1.45 tff(2941,plain,
% 1.24/1.45 (r(z, s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[128, 2940])).
% 1.24/1.45 tff(2942,plain,
% 1.24/1.45 (~r(s(z), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[309, 2941, 247, 2836])).
% 1.24/1.45 tff(2943,plain,
% 1.24/1.45 (b(s(z), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[260, 2942])).
% 1.24/1.45 tff(2944,plain,
% 1.24/1.45 (~b(z, elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[2902, 2943, 53])).
% 1.24/1.45 tff(2945,plain,
% 1.24/1.45 (z = elem!1),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[934, 2944, 2830])).
% 1.24/1.45 tff(2946,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2945])).
% 1.24/1.45 tff(2947,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(symmetry,[status(thm)],[2946])).
% 1.24/1.45 tff(2948,plain,
% 1.24/1.45 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[2947])).
% 1.24/1.45 tff(2949,plain,
% 1.24/1.45 (~r(s(z), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1768, 2941, 2836, 247])).
% 1.24/1.45 tff(2950,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1759, 2945, 2836, 81, 2949, 273])).
% 1.24/1.45 tff(2951,plain,
% 1.24/1.45 (~b(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[2950, 2948])).
% 1.24/1.45 tff(2952,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[53, 2951])).
% 1.24/1.45 tff(2953,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(2954,plain,
% 1.24/1.45 (~r(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2953, 2813, 81, 53, 80, 492])).
% 1.24/1.46 tff(2955,plain,
% 1.24/1.46 (b(s(s(s(z))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[244, 2954])).
% 1.24/1.46 tff(2956,plain,
% 1.24/1.46 (~b(z, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[646, 233, 80, 2813, 2955])).
% 1.24/1.46 tff(2957,plain,
% 1.24/1.46 (r(z, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[359, 2956])).
% 1.24/1.46 tff(2958,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2959,plain,
% 1.24/1.46 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2960,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2959])).
% 1.24/1.46 tff(2961,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2960, 2958])).
% 1.24/1.46 tff(2962,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2963,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2962, 2961])).
% 1.24/1.46 tff(2964,plain,
% 1.24/1.46 (~r(s(s(z)), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2963, 108, 2815, 2957, 2827])).
% 1.24/1.46 tff(2965,plain,
% 1.24/1.46 (b(s(s(z)), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[50, 2964])).
% 1.24/1.46 tff(2966,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2967,plain,
% 1.24/1.46 (((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2968,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2967])).
% 1.24/1.46 tff(2969,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2968, 2966])).
% 1.24/1.46 tff(2970,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2971,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2970, 2969])).
% 1.24/1.46 tff(2972,plain,
% 1.24/1.46 (~r(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2971, 108, 2815, 2957, 2827])).
% 1.24/1.46 tff(2973,plain,
% 1.24/1.46 (b(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2414, 2972])).
% 1.24/1.46 tff(2974,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2975,plain,
% 1.24/1.46 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2976,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2975])).
% 1.24/1.46 tff(2977,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[2976, 2974])).
% 1.24/1.46 tff(2978,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2979,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2978, 2977])).
% 1.24/1.46 tff(2980,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2979, 233, 442, 505, 519, 203])).
% 1.24/1.46 tff(2981,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(2982,plain,
% 1.24/1.46 (~b(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2981, 2817, 2973, 2965])).
% 1.24/1.46 tff(2983,plain,
% 1.24/1.46 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[200, 45, 2982])).
% 1.24/1.46 tff(2984,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2983, 96])).
% 1.24/1.46 tff(2985,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1864, 233, 80, 505, 1072, 519])).
% 1.24/1.46 tff(2986,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(2987,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2986, 2973, 80, 2965])).
% 1.24/1.46 tff(2988,plain,
% 1.24/1.46 (r(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1090, 2987])).
% 1.24/1.46 tff(2989,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2990,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(2991,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 1.24/1.46 tff(2992,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2991, 108, 130, 2988, 2827, 2984])).
% 1.24/1.46 tff(2993,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(2994,plain,
% 1.24/1.46 (~r(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2993, 80, 130, 53, 81])).
% 1.24/1.46 tff(2995,plain,
% 1.24/1.46 (b(s(s(s(z))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[340, 2994])).
% 1.24/1.46 tff(2996,plain,
% 1.24/1.46 (~b(s(z), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2761, 233, 2753, 53, 2751])).
% 1.24/1.46 tff(2997,plain,
% 1.24/1.46 (r(s(z), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[260, 2996])).
% 1.24/1.46 tff(2998,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(2999,plain,
% 1.24/1.46 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3000,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[2999])).
% 1.24/1.46 tff(3001,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3000, 2998])).
% 1.24/1.46 tff(3002,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3003,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 1.24/1.46 tff(3004,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3003, 108, 97, 81, 2337, 246])).
% 1.24/1.46 tff(3005,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(3006,plain,
% 1.24/1.46 (~r(s(z), s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3005, 97, 81, 2997])).
% 1.24/1.46 tff(3007,plain,
% 1.24/1.46 (b(s(z), s(s(s(z))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[325, 3006])).
% 1.24/1.46 tff(3008,plain,
% 1.24/1.46 (~b(z, s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2769, 233, 2753, 53, 2751])).
% 1.24/1.46 tff(3009,plain,
% 1.24/1.46 (r(z, s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[128, 3008])).
% 1.24/1.46 tff(3010,plain,
% 1.24/1.46 (~r(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2779, 3009, 97, 2997])).
% 1.24/1.46 tff(3011,plain,
% 1.24/1.46 (b(s(s(s(z))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1090, 3010])).
% 1.24/1.46 tff(3012,plain,
% 1.24/1.46 (~r(s(s(z)), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2801, 3007, 3011, 80, 3009])).
% 1.24/1.46 tff(3013,plain,
% 1.24/1.46 (b(s(s(z)), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[374, 3012])).
% 1.24/1.46 tff(3014,plain,
% 1.24/1.46 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1938, 3013, 53, 2753])).
% 1.24/1.46 tff(3015,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[462, 3014])).
% 1.24/1.46 tff(3016,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3017,plain,
% 1.24/1.46 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3018,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3017])).
% 1.24/1.46 tff(3019,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3018, 3016])).
% 1.24/1.46 tff(3020,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3021,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 1.24/1.46 tff(3022,plain,
% 1.24/1.46 (~b(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3021, 233, 284, 80, 285])).
% 1.24/1.46 tff(3023,plain,
% 1.24/1.46 (r(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[2414, 3022])).
% 1.24/1.46 tff(3024,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3025,plain,
% 1.24/1.46 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3026,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3025])).
% 1.24/1.46 tff(3027,plain,
% 1.24/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3026, 3024])).
% 1.24/1.46 tff(3028,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3029,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3028, 3027])).
% 1.24/1.46 tff(3030,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3029, 108, 680, 491, 3023])).
% 1.24/1.46 tff(3031,plain,
% 1.24/1.46 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[200, 45, 3030])).
% 1.24/1.46 tff(3032,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3031, 96])).
% 1.24/1.46 tff(3033,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3034,plain,
% 1.24/1.46 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3035,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[3034])).
% 1.24/1.46 tff(3036,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[3035, 3033])).
% 1.24/1.46 tff(3037,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(3038,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 1.24/1.46 tff(3039,plain,
% 1.24/1.46 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[3038, 233, 1072, 2854, 504])).
% 1.24/1.46 tff(3040,plain,
% 1.24/1.46 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[759, 3039])).
% 1.24/1.46 tff(3041,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3042,plain,
% 1.24/1.46 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(3043,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3042])).
% 1.24/1.47 tff(3044,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3043, 3041])).
% 1.24/1.47 tff(3045,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3046,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3045, 3044])).
% 1.24/1.47 tff(3047,plain,
% 1.24/1.47 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3046, 233, 1072, 2854, 504])).
% 1.24/1.47 tff(3048,plain,
% 1.24/1.47 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[598, 3047])).
% 1.24/1.47 tff(3049,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3050,plain,
% 1.24/1.47 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3051,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3050])).
% 1.24/1.47 tff(3052,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3051, 3049])).
% 1.24/1.47 tff(3053,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3054,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 1.24/1.47 tff(3055,plain,
% 1.24/1.47 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3054, 233, 2854, 504, 203])).
% 1.24/1.47 tff(3056,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[745, 3055])).
% 1.24/1.47 tff(3057,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3058,plain,
% 1.24/1.47 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3059,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3058])).
% 1.24/1.47 tff(3060,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3059, 3057])).
% 1.24/1.47 tff(3061,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3062,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.24/1.47 tff(3063,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3062, 108, 130, 2849, 1537, 727])).
% 1.24/1.47 tff(3064,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(3065,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3064, 3056, 3048, 130, 3040])).
% 1.24/1.47 tff(3066,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(3067,plain,
% 1.24/1.47 (~b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3066, 3032, 2854, 130, 1072])).
% 1.24/1.47 tff(3068,plain,
% 1.24/1.47 (r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[556, 3067, 91])).
% 1.24/1.47 tff(3069,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3070,plain,
% 1.24/1.47 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3071,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3070])).
% 1.24/1.47 tff(3072,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3071, 3069])).
% 1.24/1.47 tff(3073,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3074,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 1.24/1.47 tff(3075,plain,
% 1.24/1.47 (~r(s(s(s(s(s(z))))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3074, 108, 98, 246, 3068])).
% 1.24/1.47 tff(3076,plain,
% 1.24/1.47 (b(s(s(s(s(s(z))))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[517, 45, 514, 3075])).
% 1.24/1.47 tff(3077,plain,
% 1.24/1.47 (~b(s(s(z)), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2188, 233, 284, 80, 285])).
% 1.24/1.47 tff(3078,plain,
% 1.24/1.47 (r(s(s(z)), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[50, 3077])).
% 1.24/1.47 tff(3079,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3080,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3081,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3080, 3079])).
% 1.24/1.47 tff(3082,plain,
% 1.24/1.47 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3081, 108, 3078, 246, 3068])).
% 1.24/1.47 tff(3083,plain,
% 1.24/1.47 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[535, 45, 532, 3082])).
% 1.24/1.47 tff(3084,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3085,plain,
% 1.24/1.47 (((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3086,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3085])).
% 1.24/1.47 tff(3087,plain,
% 1.24/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3086, 3084])).
% 1.24/1.47 tff(3088,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3089,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 1.24/1.47 tff(3090,plain,
% 1.24/1.47 (~r(z, s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3089, 108, 3078, 98, 3023])).
% 1.24/1.47 tff(3091,plain,
% 1.24/1.47 (b(z, s(s(z)))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[359, 3090])).
% 1.24/1.47 tff(3092,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3093,plain,
% 1.24/1.47 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3094,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3093])).
% 1.24/1.47 tff(3095,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3094, 3092])).
% 1.24/1.47 tff(3096,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3097,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 1.24/1.47 tff(3098,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3097, 233, 80, 3091, 3083, 3076])).
% 1.24/1.47 tff(3099,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(3100,plain,
% 1.24/1.47 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3099, 3015, 3009, 2997, 2751, 130, 3011, 80, 3007, 2995])).
% 1.24/1.47 tff(3101,plain,
% 1.24/1.47 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[440, 3100])).
% 1.24/1.47 tff(3102,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[2106, 233, 3013, 3101, 2753, 53])).
% 1.24/1.47 tff(3103,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(3104,plain,
% 1.24/1.47 (~r(z, s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3103, 80, 130, 53, 81])).
% 1.24/1.47 tff(3105,plain,
% 1.24/1.47 (b(z, s(s(s(z))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[78, 3104])).
% 1.24/1.47 tff(3106,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3107,plain,
% 1.24/1.47 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3108,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3107])).
% 1.24/1.47 tff(3109,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[3108, 3106])).
% 1.24/1.47 tff(3110,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(3111,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[3110, 3109])).
% 1.24/1.47 tff(3112,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3111, 233, 273, 53, 2751, 402])).
% 1.24/1.47 tff(3113,plain,((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(3114,plain,
% 1.24/1.47 (~b(s(z), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[3113, 3105, 53])).
% 1.24/1.47 tff(3115,plain,
% 1.24/1.47 (r(s(z), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[260, 3114])).
% 1.24/1.47 tff(3116,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3117,plain,
% 1.24/1.47 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(3118,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[3117])).
% 1.24/1.47 tff(3119,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3118, 3116])).
% 1.24/1.48 tff(3120,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3121,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3120, 3119])).
% 1.24/1.48 tff(3122,plain,
% 1.24/1.48 (~b(z, s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3121, 233, 2995, 80, 3105])).
% 1.24/1.48 tff(3123,plain,
% 1.24/1.48 (r(z, s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[359, 3122])).
% 1.24/1.48 tff(3124,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3125,plain,
% 1.24/1.48 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3126,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3125])).
% 1.24/1.48 tff(3127,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3126, 3124])).
% 1.24/1.48 tff(3128,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3129,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3128, 3127])).
% 1.24/1.48 tff(3130,plain,
% 1.24/1.48 (~b(s(s(z)), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3129, 233, 2995, 80, 3105])).
% 1.24/1.48 tff(3131,plain,
% 1.24/1.48 (r(s(s(z)), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[374, 3130])).
% 1.24/1.48 tff(3132,plain,
% 1.24/1.48 (~r(s(s(z)), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2963, 108, 3131, 3123, 3115])).
% 1.24/1.48 tff(3133,plain,
% 1.24/1.48 (b(s(s(z)), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[50, 3132])).
% 1.24/1.48 tff(3134,plain,
% 1.24/1.48 (~r(s(z), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2971, 108, 3131, 3123, 3115])).
% 1.24/1.48 tff(3135,plain,
% 1.24/1.48 (b(s(z), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2414, 3134])).
% 1.24/1.48 tff(3136,plain,
% 1.24/1.48 (~b(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2986, 3133, 80, 3135])).
% 1.24/1.48 tff(3137,plain,
% 1.24/1.48 (r(s(s(s(z))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1090, 3136])).
% 1.24/1.48 tff(3138,plain,
% 1.24/1.48 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3139,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3138])).
% 1.24/1.48 tff(3140,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3139, 3016])).
% 1.24/1.48 tff(3141,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3142,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3141, 3140])).
% 1.24/1.48 tff(3143,plain,
% 1.24/1.48 (~b(s(z), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3142, 233, 2995, 80, 3135])).
% 1.24/1.48 tff(3144,plain,
% 1.24/1.48 (r(s(z), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[325, 3143])).
% 1.24/1.48 tff(3145,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3146,plain,
% 1.24/1.48 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3147,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3146])).
% 1.24/1.48 tff(3148,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3147, 3145])).
% 1.24/1.48 tff(3149,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3150,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 1.24/1.48 tff(3151,plain,
% 1.24/1.48 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3150, 108, 130, 81, 3144])).
% 1.24/1.48 tff(3152,plain,
% 1.24/1.48 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[200, 45, 3151])).
% 1.24/1.48 tff(3153,plain,
% 1.24/1.48 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3152, 96])).
% 1.24/1.48 tff(3154,plain,
% 1.24/1.48 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2981, 3153, 3135, 3133])).
% 1.24/1.48 tff(3155,plain,
% 1.24/1.48 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[462, 3154])).
% 1.24/1.48 tff(3156,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3157,plain,
% 1.24/1.48 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3158,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3157])).
% 1.24/1.48 tff(3159,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3158, 3156])).
% 1.24/1.48 tff(3160,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3161,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3160, 3159])).
% 1.24/1.48 tff(3162,plain,
% 1.24/1.48 (~r(z, s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3161, 108, 3131, 3123, 3155])).
% 1.24/1.48 tff(3163,plain,
% 1.24/1.48 (b(z, s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[222, 3162])).
% 1.24/1.48 tff(3164,plain,
% 1.24/1.48 (~b(z, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2769, 233, 3163, 53, 2751])).
% 1.24/1.48 tff(3165,plain,
% 1.24/1.48 (r(z, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[128, 3164])).
% 1.24/1.48 tff(3166,plain,
% 1.24/1.48 (~r(s(s(s(z))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[309, 3165, 3137, 3115])).
% 1.24/1.48 tff(3167,plain,
% 1.24/1.48 (b(s(s(s(z))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[244, 3166])).
% 1.24/1.48 tff(3168,plain,
% 1.24/1.48 (~r(s(s(s(s(s(z))))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3074, 108, 98, 246, 747])).
% 1.24/1.48 tff(3169,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[517, 45, 514, 3168])).
% 1.24/1.48 tff(3170,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3171,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3172,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3171, 3170])).
% 1.24/1.48 tff(3173,plain,
% 1.24/1.48 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3172, 108, 92, 246, 747])).
% 1.24/1.48 tff(3174,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[598, 3173])).
% 1.24/1.48 tff(3175,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2701, 233, 273, 272, 3174, 3169])).
% 1.24/1.48 tff(3176,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(3177,plain,
% 1.24/1.48 (~r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3176, 3167, 3165, 3105, 3115, 3137])).
% 1.24/1.48 tff(3178,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[556, 3177, 91])).
% 1.24/1.48 tff(3179,plain,
% 1.24/1.48 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[525, 233, 2995, 80, 3135, 3178, 3133])).
% 1.24/1.48 tff(3180,plain,
% 1.24/1.48 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[535, 45, 532, 3179])).
% 1.24/1.48 tff(3181,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3182,plain,
% 1.24/1.48 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3183,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3182])).
% 1.24/1.48 tff(3184,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3183, 3181])).
% 1.24/1.48 tff(3185,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3186,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3185, 3184])).
% 1.24/1.48 tff(3187,plain,
% 1.24/1.48 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3186, 233, 3135, 3178, 3153])).
% 1.24/1.48 tff(3188,plain,
% 1.24/1.48 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[579, 45, 576, 3187])).
% 1.24/1.48 tff(3189,plain,
% 1.24/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3190,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3191,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3190, 3189])).
% 1.24/1.48 tff(3192,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3191, 108, 3131, 3155, 3188, 3180])).
% 1.24/1.48 tff(3193,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(3194,plain,
% 1.24/1.48 (~b(s(s(z)), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3193, 130, 53, 81])).
% 1.24/1.48 tff(3195,plain,
% 1.24/1.48 (r(s(s(z)), s(s(s(z))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2228, 3194])).
% 1.24/1.48 tff(3196,plain,
% 1.24/1.48 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2598, 3195, 130, 81])).
% 1.24/1.48 tff(3197,plain,
% 1.24/1.48 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[440, 3196])).
% 1.24/1.48 tff(3198,plain,
% 1.24/1.48 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2489, 3195, 130, 81])).
% 1.24/1.48 tff(3199,plain,
% 1.24/1.48 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[462, 3198])).
% 1.24/1.48 tff(3200,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3201,plain,
% 1.24/1.48 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3202,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[3201])).
% 1.24/1.48 tff(3203,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[3202, 3200])).
% 1.24/1.48 tff(3204,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(3205,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.24/1.48 tff(3206,plain,
% 1.24/1.48 (~b(s(z), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[3205, 233, 3199, 3197, 2751])).
% 1.24/1.48 tff(3207,plain,
% 1.24/1.48 (r(s(z), s(s(z)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[2414, 3206])).
% 1.24/1.48 tff(3208,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3209,plain,
% 1.24/1.48 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(3210,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3209])).
% 1.24/1.49 tff(3211,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3210, 3208])).
% 1.24/1.49 tff(3212,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3213,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3212, 3211])).
% 1.24/1.49 tff(3214,plain,
% 1.24/1.49 (~b(s(s(z)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3213, 233, 3199, 3197, 2751])).
% 1.24/1.49 tff(3215,plain,
% 1.24/1.49 (r(s(s(z)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[50, 3214])).
% 1.24/1.49 tff(3216,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2489, 81, 2240, 130])).
% 1.24/1.49 tff(3217,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[462, 3216])).
% 1.24/1.49 tff(3218,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3219,plain,
% 1.24/1.49 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3220,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3219])).
% 1.24/1.49 tff(3221,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3220, 3218])).
% 1.24/1.49 tff(3222,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3223,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3222, 3221])).
% 1.24/1.49 tff(3224,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3223, 108, 130, 97, 81])).
% 1.24/1.49 tff(3225,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.49 tff(3226,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.49 tff(3227,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[629, 45, 89, 3226, 3225])).
% 1.24/1.49 tff(3228,plain,(r(s(s(s(s(z)))), z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3229,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3228, 3224])).
% 1.24/1.49 tff(3230,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1938, 3229, 2753, 649, 3217])).
% 1.24/1.49 tff(3231,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3232,plain,
% 1.24/1.49 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3231, 97, 130, 649, 2240])).
% 1.24/1.49 tff(3233,plain,
% 1.24/1.49 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[186, 3232])).
% 1.24/1.49 tff(3234,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3235,plain,
% 1.24/1.49 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3236,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3235])).
% 1.24/1.49 tff(3237,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3236, 3234])).
% 1.24/1.49 tff(3238,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3239,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3238, 3237])).
% 1.24/1.49 tff(3240,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3239, 233, 53, 204, 1072, 2854])).
% 1.24/1.49 tff(3241,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3242,plain,
% 1.24/1.49 (~b(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3241, 3233, 2854, 1072])).
% 1.24/1.49 tff(3243,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3228, 3242])).
% 1.24/1.49 tff(3244,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.49 tff(3245,plain,
% 1.24/1.49 (~r(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2475, 108, 2240, 97, 81])).
% 1.24/1.49 tff(3246,plain,
% 1.24/1.49 (b(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[359, 3245])).
% 1.24/1.49 tff(3247,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3248,plain,
% 1.24/1.49 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3249,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3248])).
% 1.24/1.49 tff(3250,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3249, 3247])).
% 1.24/1.49 tff(3251,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3252,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3251, 3250])).
% 1.24/1.49 tff(3253,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3252, 233, 284, 706, 649, 272])).
% 1.24/1.49 tff(3254,plain,((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3255,plain,
% 1.24/1.49 (~b(s(s(s(z))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3254, 3246, 284, 649])).
% 1.24/1.49 tff(3256,plain,
% 1.24/1.49 (r(s(s(s(z))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[244, 3255])).
% 1.24/1.49 tff(3257,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3258,plain,
% 1.24/1.49 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3259,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3258])).
% 1.24/1.49 tff(3260,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3259, 3257])).
% 1.24/1.49 tff(3261,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3262,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3261, 3260])).
% 1.24/1.49 tff(3263,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3262, 108, 97, 3256, 81, 3244])).
% 1.24/1.49 tff(3264,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3265,plain,
% 1.24/1.49 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3264, 97, 3244, 284, 649, 2240])).
% 1.24/1.49 tff(3266,plain,
% 1.24/1.49 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[186, 3265])).
% 1.24/1.49 tff(3267,plain,
% 1.24/1.49 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2398, 3266, 284, 649])).
% 1.24/1.49 tff(3268,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[462, 3267])).
% 1.24/1.49 tff(3269,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3270,plain,
% 1.24/1.49 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3271,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[3270])).
% 1.24/1.49 tff(3272,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[3271, 3269])).
% 1.24/1.49 tff(3273,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3274,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3273, 3272])).
% 1.24/1.49 tff(3275,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3274, 108, 493, 2240, 680, 3244])).
% 1.24/1.49 tff(3276,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(3277,plain,
% 1.24/1.49 (~r(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3276, 3268, 3244, 2240])).
% 1.24/1.49 tff(3278,plain,
% 1.24/1.49 (b(z, s(s(z)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[359, 3277])).
% 1.24/1.49 tff(3279,plain,
% 1.24/1.49 (~b(s(s(s(z))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3254, 3278, 284, 649])).
% 1.24/1.49 tff(3280,plain,
% 1.24/1.49 (r(s(s(s(z))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[244, 3279])).
% 1.24/1.49 tff(3281,plain,
% 1.24/1.49 (~r(s(z), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[2360, 3278, 649, 97, 3280, 2240])).
% 1.24/1.49 tff(3282,plain,
% 1.24/1.49 (b(s(z), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[325, 3281])).
% 1.24/1.49 tff(3283,plain,
% 1.24/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3284,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(3285,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 1.24/1.49 tff(3286,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[3285, 108, 97, 3280, 3244])).
% 1.24/1.49 tff(3287,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[386, 3286])).
% 1.24/1.49 tff(3288,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(3289,plain,
% 1.24/1.49 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(3290,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[3289])).
% 1.24/1.50 tff(3291,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.50 inference(transitivity,[status(thm)],[3290, 3288])).
% 1.24/1.50 tff(3292,plain,
% 1.24/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(3293,plain,
% 1.24/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[3292, 3291])).
% 1.24/1.50 tff(3294,plain,
% 1.24/1.50 (~b(s(s(s(s(z)))), s(z))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[3293, 233, 3287, 284, 3282])).
% 1.24/1.50 tff(3295,plain,
% 1.24/1.50 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[200, 45, 3294])).
% 1.24/1.50 tff(3296,plain,
% 1.24/1.50 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[3295, 96])).
% 1.24/1.50 tff(3297,plain,
% 1.24/1.50 (~b(s(z), s(s(z)))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[2358, 233, 706, 649, 402])).
% 1.24/1.50 tff(3298,plain,
% 1.24/1.50 (r(s(z), s(s(z)))),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[481, 45, 34, 3297])).
% 1.24/1.50 tff(3299,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(3300,plain,
% 1.24/1.50 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(3301,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[3300])).
% 1.35/1.50 tff(3302,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[3301, 3299])).
% 1.35/1.50 tff(3303,plain,
% 1.35/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(3304,plain,
% 1.35/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 1.35/1.50 tff(3305,plain,
% 1.35/1.50 (~b(s(s(z)), s(z))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3304, 233, 284, 706, 649, 402, 285])).
% 1.35/1.50 tff(3306,plain,
% 1.35/1.50 (r(s(s(z)), s(z))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[48, 45, 35, 3305])).
% 1.35/1.50 tff(3307,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3308,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(3309,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.35/1.50 tff(3310,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3309, 108, 680, 3306, 188, 3298])).
% 1.35/1.50 tff(3311,plain,((~b(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3312,plain,
% 1.35/1.50 (~b(s(z), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3311, 3268, 3296, 284, 3278, 649, 3282])).
% 1.35/1.50 tff(3313,plain,
% 1.35/1.50 (r(s(z), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[260, 3312])).
% 1.35/1.50 tff(3314,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3315,plain,
% 1.35/1.50 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3316,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[3315])).
% 1.35/1.50 tff(3317,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[3316, 3314])).
% 1.35/1.50 tff(3318,plain,
% 1.35/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(3319,plain,
% 1.35/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[3318, 3317])).
% 1.35/1.50 tff(3320,plain,
% 1.35/1.50 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3319, 233, 3287, 284, 3282])).
% 1.35/1.50 tff(3321,plain,
% 1.35/1.50 (r(s(z), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1122, 3320])).
% 1.35/1.50 tff(3322,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3323,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(3324,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 1.35/1.50 tff(3325,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3324, 108, 97, 3244, 3321, 3313])).
% 1.35/1.50 tff(3326,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3327,plain,
% 1.35/1.50 (~b(s(s(s(z))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3326, 3243, 649, 97, 2240])).
% 1.35/1.50 tff(3328,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3329,plain,
% 1.35/1.50 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3330,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[3329])).
% 1.35/1.50 tff(3331,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[3330, 3328])).
% 1.35/1.50 tff(3332,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(3333,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[3332, 3331])).
% 1.35/1.50 tff(3334,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3333, 108, 130, 492, 97, 3244])).
% 1.35/1.50 tff(3335,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3336,plain,
% 1.35/1.50 (~r(s(s(s(z))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3335, 3243, 130, 97])).
% 1.35/1.50 tff(3337,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[340, 3336, 3327])).
% 1.35/1.50 tff(3338,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3339,plain,
% 1.35/1.50 (~b(s(s(z)), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3338, 130, 97, 2240, 2854, 1072])).
% 1.35/1.50 tff(3340,plain,
% 1.35/1.50 (r(s(s(z)), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[374, 3339])).
% 1.35/1.50 tff(3341,plain,
% 1.35/1.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[2612, 3340, 2240, 97])).
% 1.35/1.50 tff(3342,plain,
% 1.35/1.50 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[186, 3341])).
% 1.35/1.50 tff(3343,plain,
% 1.35/1.50 (~b(s(s(s(s(z)))), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3241, 204, 2854, 1072])).
% 1.35/1.50 tff(3344,plain,
% 1.35/1.50 (r(s(s(s(s(z)))), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3228, 3343])).
% 1.35/1.50 tff(3345,plain,
% 1.35/1.50 (~r(s(s(s(z))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3335, 97, 130, 3244])).
% 1.35/1.50 tff(3346,plain,
% 1.35/1.50 (b(s(s(s(z))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[340, 3345])).
% 1.35/1.50 tff(3347,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3348,plain,
% 1.35/1.50 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3349,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[3348])).
% 1.35/1.50 tff(3350,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[3349, 3347])).
% 1.35/1.50 tff(3351,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(3352,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[3351, 3350])).
% 1.35/1.50 tff(3353,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3352, 108, 701, 97, 680, 3244])).
% 1.35/1.50 tff(3354,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3355,plain,
% 1.35/1.50 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3354, 97, 3244, 701])).
% 1.35/1.50 tff(3356,plain,
% 1.35/1.50 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[462, 3355])).
% 1.35/1.50 tff(3357,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3358,plain,
% 1.35/1.50 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3359,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[3358])).
% 1.35/1.50 tff(3360,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[3359, 3357])).
% 1.35/1.50 tff(3361,plain,
% 1.35/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(3362,plain,
% 1.35/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[3361, 3360])).
% 1.35/1.50 tff(3363,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3362, 233, 284, 442, 424, 204])).
% 1.35/1.50 tff(3364,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3365,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3364, 3356, 3346, 424, 204])).
% 1.35/1.50 tff(3366,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3367,plain,
% 1.35/1.50 (~r(z, s(s(s(z))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3366, 204, 424, 3344, 701, 130])).
% 1.35/1.50 tff(3368,plain,
% 1.35/1.50 (b(z, s(s(s(z))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[78, 3367])).
% 1.35/1.50 tff(3369,plain,
% 1.35/1.50 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3364, 284, 424, 204])).
% 1.35/1.50 tff(3370,plain,
% 1.35/1.50 (r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[462, 3369])).
% 1.35/1.50 tff(3371,plain,
% 1.35/1.50 (~b(z, s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[2572, 284, 424, 273])).
% 1.35/1.50 tff(3372,plain,
% 1.35/1.50 (r(z, s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[359, 3371])).
% 1.35/1.50 tff(3373,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3276, 3372, 3370, 2240, 3244])).
% 1.35/1.50 tff(3374,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(3375,plain,
% 1.35/1.50 (~b(s(s(s(z))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3374, 3344, 2240, 424, 3368, 204])).
% 1.35/1.50 tff(3376,plain,
% 1.35/1.50 (r(s(s(s(z))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[340, 3375])).
% 1.35/1.50 tff(3377,plain,
% 1.35/1.50 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[2510, 3376, 130, 701])).
% 1.35/1.50 tff(3378,plain,
% 1.35/1.50 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[462, 3377])).
% 1.35/1.50 tff(3379,plain,
% 1.35/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(3380,plain,
% 1.35/1.50 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3381,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[3380])).
% 1.35/1.51 tff(3382,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[3381, 3379])).
% 1.35/1.51 tff(3383,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(3384,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[3383, 3382])).
% 1.35/1.51 tff(3385,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3384, 233, 3378, 204, 1072, 2854])).
% 1.35/1.51 tff(3386,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(3387,plain,
% 1.35/1.51 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3386, 701, 2854, 130, 1072, 2240, 424])).
% 1.35/1.51 tff(3388,plain,
% 1.35/1.51 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[186, 3387])).
% 1.35/1.51 tff(3389,plain,
% 1.35/1.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2489, 3388, 2240, 130])).
% 1.35/1.51 tff(3390,plain,
% 1.35/1.51 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[462, 3389])).
% 1.35/1.51 tff(3391,plain,
% 1.35/1.51 (~b(s(z), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3205, 233, 3390, 424, 2854])).
% 1.35/1.51 tff(3392,plain,
% 1.35/1.51 (r(s(z), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[481, 45, 34, 3391])).
% 1.35/1.51 tff(3393,plain,
% 1.35/1.51 (~r(z, s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2612, 3388, 2240, 701])).
% 1.35/1.51 tff(3394,plain,
% 1.35/1.51 (b(z, s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[78, 3393])).
% 1.35/1.51 tff(3395,plain,
% 1.35/1.51 (~b(s(s(z)), s(z))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3213, 233, 3390, 424, 2854])).
% 1.35/1.51 tff(3396,plain,
% 1.35/1.51 (r(s(s(z)), s(z))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[48, 45, 35, 3395])).
% 1.35/1.51 tff(3397,plain,
% 1.35/1.51 (~b(s(z), s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2213, 701, 3396, 3394, 1072])).
% 1.35/1.51 tff(3398,plain,
% 1.35/1.51 (r(s(z), s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[325, 3397])).
% 1.35/1.51 tff(3399,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3400,plain,
% 1.35/1.51 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3401,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[3400])).
% 1.35/1.51 tff(3402,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[3401, 3399])).
% 1.35/1.51 tff(3403,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(3404,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[3403, 3402])).
% 1.35/1.51 tff(3405,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3404, 108, 2240, 3388, 3398, 3392])).
% 1.35/1.51 tff(3406,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(3407,plain,
% 1.35/1.51 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3406, 3340, 1072, 130, 2854, 2240])).
% 1.35/1.51 tff(3408,plain,
% 1.35/1.51 (r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[440, 3407])).
% 1.35/1.51 tff(3409,plain,
% 1.35/1.51 (~r(s(s(s(z))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2586, 3408, 2240, 130])).
% 1.35/1.51 tff(3410,plain,
% 1.35/1.51 (b(s(s(s(z))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[244, 3409])).
% 1.35/1.51 tff(3411,plain,
% 1.35/1.51 (~b(s(s(s(s(z)))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1906, 706, 272, 204])).
% 1.35/1.51 tff(3412,plain,
% 1.35/1.51 (r(s(s(s(s(z)))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3228, 3411])).
% 1.35/1.51 tff(3413,plain,
% 1.35/1.51 (~r(s(s(s(z))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3335, 3412, 97, 130])).
% 1.35/1.51 tff(3414,plain,
% 1.35/1.51 (b(s(s(s(z))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[340, 3413])).
% 1.35/1.51 tff(3415,plain,
% 1.35/1.51 (~b(s(s(z)), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3254, 3414, 706, 272])).
% 1.35/1.51 tff(3416,plain,
% 1.35/1.51 (r(s(s(z)), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[374, 3415])).
% 1.35/1.51 tff(3417,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3418,plain,
% 1.35/1.51 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3419,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[3418])).
% 1.35/1.51 tff(3420,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[3419, 3417])).
% 1.35/1.51 tff(3421,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(3422,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 1.35/1.51 tff(3423,plain,
% 1.35/1.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3422, 108, 3416, 97, 3412])).
% 1.35/1.51 tff(3424,plain,
% 1.35/1.51 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[440, 3423])).
% 1.35/1.51 tff(3425,plain,
% 1.35/1.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3354, 3416, 97, 3412])).
% 1.35/1.51 tff(3426,plain,
% 1.35/1.51 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[462, 3425])).
% 1.35/1.51 tff(3427,plain,
% 1.35/1.51 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3428,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[3427])).
% 1.35/1.51 tff(3429,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[3428, 3357])).
% 1.35/1.51 tff(3430,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(3431,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[3430, 3429])).
% 1.35/1.51 tff(3432,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3431, 233, 3414, 3426, 3424, 204])).
% 1.35/1.51 tff(3433,plain,((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(3434,plain,
% 1.35/1.51 (~b(z, s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3433, 3410, 97, 130, 3342])).
% 1.35/1.51 tff(3435,plain,
% 1.35/1.51 (~b(s(s(s(s(z)))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3241, 3342, 2854, 1072])).
% 1.35/1.51 tff(3436,plain,
% 1.35/1.51 (r(s(s(s(s(z)))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3228, 3435])).
% 1.35/1.51 tff(3437,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3438,plain,
% 1.35/1.51 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3439,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[3438])).
% 1.35/1.51 tff(3440,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[3439, 3437])).
% 1.35/1.51 tff(3441,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(3442,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[3441, 3440])).
% 1.35/1.51 tff(3443,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3442, 108, 701, 493, 491, 3244])).
% 1.35/1.51 tff(3444,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(3445,plain,
% 1.35/1.51 (~r(z, s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3444, 3436, 3408, 3340])).
% 1.35/1.51 tff(3446,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[359, 3445, 3434])).
% 1.35/1.51 tff(3447,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(3448,plain,
% 1.35/1.51 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3447, 97, 2854, 1072, 2240])).
% 1.35/1.51 tff(3449,plain,
% 1.35/1.51 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[386, 3448])).
% 1.35/1.51 tff(3450,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3451,plain,
% 1.35/1.51 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3452,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[3451])).
% 1.35/1.51 tff(3453,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[3452, 3450])).
% 1.35/1.51 tff(3454,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(3455,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.35/1.51 tff(3456,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3455, 233, 389, 204, 1072, 2854])).
% 1.35/1.51 tff(3457,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(3458,plain,
% 1.35/1.51 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3457, 3449, 1072, 2854])).
% 1.35/1.51 tff(3459,plain,
% 1.35/1.51 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[186, 3458])).
% 1.35/1.51 tff(3460,plain,
% 1.35/1.51 (~r(z, s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2475, 108, 2240, 97, 3459])).
% 1.35/1.51 tff(3461,plain,
% 1.35/1.51 (b(z, s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[359, 3460])).
% 1.35/1.51 tff(3462,plain,
% 1.35/1.51 (~r(s(s(z)), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2612, 3459, 2240, 97])).
% 1.35/1.51 tff(3463,plain,
% 1.35/1.51 (b(s(s(z)), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[374, 3462])).
% 1.35/1.51 tff(3464,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3465,plain,
% 1.35/1.51 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(3466,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[3465])).
% 1.35/1.51 tff(3467,plain,
% 1.35/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[3466, 3464])).
% 1.35/1.51 tff(3468,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(3469,plain,
% 1.35/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[3468, 3467])).
% 1.35/1.51 tff(3470,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3469, 233, 389, 1072, 2854, 285])).
% 1.35/1.51 tff(3471,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(3472,plain,
% 1.35/1.51 (~b(s(z), s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3471, 3449, 1072, 2854])).
% 1.35/1.51 tff(3473,plain,
% 1.35/1.51 (r(s(z), s(s(s(z))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[325, 3472])).
% 1.35/1.51 tff(3474,plain,
% 1.35/1.51 (~r(s(s(s(z))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2360, 3461, 2240, 97, 3473, 3463])).
% 1.35/1.51 tff(3475,plain,
% 1.35/1.51 (b(s(s(s(z))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[244, 3474])).
% 1.35/1.51 tff(3476,plain,
% 1.35/1.51 (~b(s(s(s(z))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3254, 3475, 3463, 3461])).
% 1.35/1.51 tff(3477,plain,
% 1.35/1.51 (r(s(s(s(z))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[340, 3476])).
% 1.35/1.51 tff(3478,plain,
% 1.35/1.51 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[688, 491, 492, 81])).
% 1.35/1.51 tff(3479,plain,
% 1.35/1.51 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[462, 3478])).
% 1.35/1.52 tff(3480,plain,
% 1.35/1.52 (~b(s(s(s(s(z)))), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2258, 3479, 649, 706])).
% 1.35/1.52 tff(3481,plain,
% 1.35/1.52 (r(s(s(s(s(z)))), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3228, 3480])).
% 1.35/1.52 tff(3482,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3483,plain,
% 1.35/1.52 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3484,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[3483])).
% 1.35/1.52 tff(3485,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[3484, 3482])).
% 1.35/1.52 tff(3486,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(3487,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 1.35/1.52 tff(3488,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3487, 108, 2240, 491, 81, 3481])).
% 1.35/1.52 tff(3489,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(3490,plain,
% 1.35/1.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3489, 3459, 2240, 3463, 3461, 3477])).
% 1.35/1.52 tff(3491,plain,
% 1.35/1.52 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[440, 3490])).
% 1.35/1.52 tff(3492,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3493,plain,
% 1.35/1.52 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3494,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[3493])).
% 1.35/1.52 tff(3495,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[3494, 3492])).
% 1.35/1.52 tff(3496,plain,
% 1.35/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(3497,plain,
% 1.35/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[3496, 3495])).
% 1.35/1.52 tff(3498,plain,
% 1.35/1.52 (~b(s(z), s(s(z)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3497, 233, 3449, 3491, 2854])).
% 1.35/1.52 tff(3499,plain,
% 1.35/1.52 (r(s(z), s(s(z)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[481, 45, 34, 3498])).
% 1.35/1.52 tff(3500,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3501,plain,
% 1.35/1.52 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3502,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[3501])).
% 1.35/1.52 tff(3503,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[3502, 3500])).
% 1.35/1.52 tff(3504,plain,
% 1.35/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(3505,plain,
% 1.35/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[3504, 3503])).
% 1.35/1.52 tff(3506,plain,
% 1.35/1.52 (~b(s(s(z)), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3505, 233, 3449, 3491, 2854])).
% 1.35/1.52 tff(3507,plain,
% 1.35/1.52 (r(s(s(z)), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[48, 45, 35, 3506])).
% 1.35/1.52 tff(3508,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3509,plain,
% 1.35/1.52 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3510,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[3509])).
% 1.35/1.52 tff(3511,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[3510, 3508])).
% 1.35/1.52 tff(3512,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(3513,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[3512, 3511])).
% 1.35/1.52 tff(3514,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3513, 108, 3477, 3473, 3507, 3499])).
% 1.35/1.52 tff(3515,plain,((~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(3516,plain,
% 1.35/1.52 (~r(z, s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3515, 1072, 2240, 2854])).
% 1.35/1.52 tff(3517,plain,
% 1.35/1.52 (b(z, s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[78, 3516])).
% 1.35/1.52 tff(3518,plain,
% 1.35/1.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2530, 53, 3517, 1072])).
% 1.35/1.52 tff(3519,plain,
% 1.35/1.52 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[386, 3518])).
% 1.35/1.52 tff(3520,plain,
% 1.35/1.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2598, 3519, 2240, 81])).
% 1.35/1.52 tff(3521,plain,
% 1.35/1.52 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[440, 3520])).
% 1.35/1.52 tff(3522,plain,
% 1.35/1.52 (~r(s(s(z)), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3406, 3521, 1072, 3519, 2854, 2240])).
% 1.35/1.52 tff(3523,plain,
% 1.35/1.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2489, 3519, 2240, 81])).
% 1.35/1.52 tff(3524,plain,
% 1.35/1.52 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[462, 3523])).
% 1.35/1.52 tff(3525,plain,
% 1.35/1.52 (~b(s(s(z)), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[677, 3524, 3517, 53])).
% 1.35/1.52 tff(3526,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[374, 3525, 3522])).
% 1.35/1.52 tff(3527,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(3528,plain,
% 1.35/1.52 (~b(s(s(s(z))), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3527, 3195, 53, 2751, 81])).
% 1.35/1.52 tff(3529,plain,
% 1.35/1.52 (r(s(s(s(z))), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1090, 3528])).
% 1.35/1.52 tff(3530,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3531,plain,
% 1.35/1.52 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3532,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[3531])).
% 1.35/1.52 tff(3533,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[3532, 3530])).
% 1.35/1.52 tff(3534,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(3535,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.35/1.52 tff(3536,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3535, 108, 3195, 3529, 3215, 3207])).
% 1.35/1.52 tff(3537,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(3538,plain,
% 1.35/1.52 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3537, 53, 81])).
% 1.35/1.52 tff(3539,plain,
% 1.35/1.52 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[386, 3538])).
% 1.35/1.52 tff(3540,plain,
% 1.35/1.52 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3537, 81, 53])).
% 1.35/1.52 tff(3541,plain,
% 1.35/1.52 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[386, 3540])).
% 1.35/1.52 tff(3542,plain,
% 1.35/1.52 (~b(z, s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2530, 1072, 53, 3541])).
% 1.35/1.52 tff(3543,plain,
% 1.35/1.52 (r(z, s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[78, 3542])).
% 1.35/1.52 tff(3544,plain,
% 1.35/1.52 (~b(s(z), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3471, 1072, 2751, 3541])).
% 1.35/1.52 tff(3545,plain,
% 1.35/1.52 (r(s(z), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[325, 3544])).
% 1.35/1.52 tff(3546,plain,
% 1.35/1.52 (~r(s(z), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3005, 3545, 81, 3543])).
% 1.35/1.52 tff(3547,plain,
% 1.35/1.52 (b(s(z), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[260, 3546])).
% 1.35/1.52 tff(3548,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.35/1.52 tff(3549,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3550,plain,
% 1.35/1.52 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3551,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[3550])).
% 1.35/1.52 tff(3552,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[3551, 3549])).
% 1.35/1.52 tff(3553,plain,
% 1.35/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(3554,plain,
% 1.35/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 1.35/1.52 tff(3555,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3554, 233, 53, 2751, 402, 3548])).
% 1.35/1.52 tff(3556,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(3557,plain,
% 1.35/1.52 (~b(z, s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3556, 3547, 53])).
% 1.35/1.52 tff(3558,plain,
% 1.35/1.52 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2864, 45, 3557])).
% 1.35/1.52 tff(3559,plain,
% 1.35/1.52 (r(z, s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3558, 2853])).
% 1.35/1.52 tff(3560,plain,
% 1.35/1.52 (~r(s(s(z)), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2612, 97, 81, 2240])).
% 1.35/1.52 tff(3561,plain,
% 1.35/1.52 (b(s(s(z)), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[374, 3560])).
% 1.35/1.52 tff(3562,plain,
% 1.35/1.52 (~r(z, s(s(z)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2477, 97, 81, 2240])).
% 1.35/1.52 tff(3563,plain,
% 1.35/1.52 (b(z, s(s(z)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[359, 3562])).
% 1.35/1.52 tff(3564,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2467, 3563, 3561, 81, 2240, 53])).
% 1.35/1.52 tff(3565,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(3566,plain,
% 1.35/1.52 (~r(z, s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3565, 2240, 81, 53])).
% 1.35/1.52 tff(3567,plain,
% 1.35/1.52 (b(z, s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[78, 3566])).
% 1.35/1.52 tff(3568,plain,
% 1.35/1.52 (~b(s(z), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3113, 3567, 53])).
% 1.35/1.52 tff(3569,plain,
% 1.35/1.52 (r(s(z), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[260, 3568])).
% 1.35/1.52 tff(3570,plain,
% 1.35/1.52 (~b(s(s(s(z))), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3527, 2240, 53, 2751, 81])).
% 1.35/1.52 tff(3571,plain,
% 1.35/1.52 (r(s(s(s(z))), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1090, 3570])).
% 1.35/1.52 tff(3572,plain,
% 1.35/1.52 (~b(s(s(s(z))), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2691, 3567, 3541, 53])).
% 1.35/1.52 tff(3573,plain,
% 1.35/1.52 (r(s(s(s(z))), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[244, 3572])).
% 1.35/1.52 tff(3574,plain,
% 1.35/1.52 (~r(z, s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[309, 3573, 3571, 3569])).
% 1.35/1.52 tff(3575,plain,
% 1.35/1.52 (b(z, s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[128, 3574])).
% 1.35/1.52 tff(3576,plain,
% 1.35/1.52 (~r(z, s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[986, 3573, 3569, 3571])).
% 1.35/1.52 tff(3577,plain,
% 1.35/1.52 (b(z, s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[222, 3576])).
% 1.35/1.52 tff(3578,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3579,plain,
% 1.35/1.52 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(3580,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[3579])).
% 1.35/1.52 tff(3581,plain,
% 1.35/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[3580, 3578])).
% 1.35/1.53 tff(3582,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(3583,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[3582, 3581])).
% 1.35/1.53 tff(3584,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3583, 233, 389, 1930, 2854, 388])).
% 1.35/1.53 tff(3585,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(3586,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3585, 3577, 3575, 2751, 3541])).
% 1.35/1.53 tff(3587,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(3588,plain,
% 1.35/1.53 (~r(s(s(z)), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3587, 81, 53])).
% 1.35/1.53 tff(3589,plain,
% 1.35/1.53 (b(s(s(z)), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2228, 3588])).
% 1.35/1.53 tff(3590,plain,
% 1.35/1.53 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1844, 1072, 3541, 3589])).
% 1.35/1.53 tff(3591,plain,
% 1.35/1.53 (r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[440, 3590])).
% 1.35/1.53 tff(3592,plain,
% 1.35/1.53 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1852, 233, 3541, 3589, 1072])).
% 1.35/1.53 tff(3593,plain,
% 1.35/1.53 (r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[462, 3592])).
% 1.35/1.53 tff(3594,plain,
% 1.35/1.53 (~r(s(s(s(z))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[688, 3593, 3591, 81])).
% 1.35/1.53 tff(3595,plain,
% 1.35/1.53 (b(s(s(s(z))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[340, 3594])).
% 1.35/1.53 tff(3596,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3597,plain,
% 1.35/1.53 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3598,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[3597])).
% 1.35/1.53 tff(3599,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[3598, 3596])).
% 1.35/1.53 tff(3600,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(3601,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[3600, 3599])).
% 1.35/1.53 tff(3602,plain,
% 1.35/1.53 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3601, 233, 284, 80, 1547])).
% 1.35/1.53 tff(3603,plain,
% 1.35/1.53 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[535, 45, 532, 3602])).
% 1.35/1.53 tff(3604,plain,
% 1.35/1.53 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[605, 233, 389, 284, 1547])).
% 1.35/1.53 tff(3605,plain,
% 1.35/1.53 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[579, 45, 576, 3604])).
% 1.35/1.53 tff(3606,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3607,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(3608,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 1.35/1.53 tff(3609,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3608, 108, 680, 491, 3605, 3603])).
% 1.35/1.53 tff(3610,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(3611,plain,
% 1.35/1.53 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3610, 3593, 3591, 3595, 3589, 3541])).
% 1.35/1.53 tff(3612,plain,
% 1.35/1.53 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[598, 3611])).
% 1.35/1.53 tff(3613,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3614,plain,
% 1.35/1.53 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3615,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[3614])).
% 1.35/1.53 tff(3616,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[3615, 3613])).
% 1.35/1.53 tff(3617,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(3618,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 1.35/1.53 tff(3619,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3618, 108, 3543, 81, 3612, 3559])).
% 1.35/1.53 tff(3620,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(3621,plain,
% 1.35/1.53 (~b(s(s(s(z))), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3620, 53, 81])).
% 1.35/1.53 tff(3622,plain,
% 1.35/1.53 (r(s(s(s(z))), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1090, 3621])).
% 1.35/1.53 tff(3623,plain,
% 1.35/1.53 (~r(s(s(s(z))), z)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[255, 246, 92, 97])).
% 1.35/1.53 tff(3624,plain,
% 1.35/1.53 (b(s(s(s(z))), z)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[244, 3623])).
% 1.35/1.53 tff(3625,plain,
% 1.35/1.53 (~r(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2779, 246, 92, 97])).
% 1.35/1.53 tff(3626,plain,
% 1.35/1.53 (b(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[128, 3625])).
% 1.35/1.53 tff(3627,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[397, 3626, 3624, 53, 389])).
% 1.35/1.53 tff(3628,plain,((~r(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(3629,plain,
% 1.35/1.53 (~r(s(z), z)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3628, 3539, 79, 3622, 53])).
% 1.35/1.53 tff(3630,plain,
% 1.35/1.53 (b(s(z), z)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[260, 3629])).
% 1.35/1.53 tff(3631,plain,
% 1.35/1.53 (~b(z, elem!1)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2902, 3630, 53])).
% 1.35/1.53 tff(3632,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3633,plain,
% 1.35/1.53 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3634,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[3633])).
% 1.35/1.53 tff(3635,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[3634, 3632])).
% 1.35/1.53 tff(3636,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(3637,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 1.35/1.53 tff(3638,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3637, 233, 389, 284, 80, 442])).
% 1.35/1.53 tff(3639,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(3640,plain,
% 1.35/1.53 (~b(s(s(s(z))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3639, 442, 389, 80])).
% 1.35/1.53 tff(3641,plain,
% 1.35/1.53 (r(s(s(s(z))), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[340, 3640])).
% 1.35/1.53 tff(3642,plain,
% 1.35/1.53 (~b(s(s(s(z))), z)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[638, 442, 389, 80])).
% 1.35/1.53 tff(3643,plain,
% 1.35/1.53 (r(s(s(s(z))), z)),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[244, 3642])).
% 1.35/1.53 tff(3644,plain,
% 1.35/1.53 (~b(z, s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2258, 649, 53, 442])).
% 1.35/1.53 tff(3645,plain,
% 1.35/1.53 (~r(s(s(z)), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2248, 493, 492, 97])).
% 1.35/1.53 tff(3646,plain,
% 1.35/1.53 (b(s(s(z)), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2228, 3645])).
% 1.35/1.53 tff(3647,plain,
% 1.35/1.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[501, 493, 492, 97])).
% 1.35/1.53 tff(3648,plain,
% 1.35/1.53 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[440, 3647])).
% 1.35/1.53 tff(3649,plain,
% 1.35/1.53 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[432, 3646, 3648, 53])).
% 1.35/1.53 tff(3650,plain,
% 1.35/1.53 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[186, 3649])).
% 1.35/1.53 tff(3651,plain,
% 1.35/1.53 (~b(s(s(s(z))), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2108, 3650, 53, 492, 97, 649, 3646])).
% 1.35/1.53 tff(3652,plain,
% 1.35/1.53 (r(s(s(s(z))), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1090, 3651])).
% 1.35/1.53 tff(3653,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3654,plain,
% 1.35/1.53 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3655,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[3654])).
% 1.35/1.53 tff(3656,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[3655, 3653])).
% 1.35/1.53 tff(3657,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(3658,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[3657, 3656])).
% 1.35/1.53 tff(3659,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3658, 233, 649, 424, 53, 388])).
% 1.35/1.53 tff(3660,plain,((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(3661,plain,
% 1.35/1.53 (~b(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3660, 3648, 649, 53])).
% 1.35/1.53 tff(3662,plain,
% 1.35/1.53 (r(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[128, 3661])).
% 1.35/1.53 tff(3663,plain,
% 1.35/1.53 (~r(s(z), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[116, 3662, 3652, 97])).
% 1.35/1.53 tff(3664,plain,
% 1.35/1.53 (b(s(z), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1122, 3663])).
% 1.35/1.53 tff(3665,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3666,plain,
% 1.35/1.53 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3667,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[3666])).
% 1.35/1.53 tff(3668,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[3667, 3665])).
% 1.35/1.53 tff(3669,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(3670,plain,
% 1.35/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 1.35/1.53 tff(3671,plain,
% 1.35/1.53 (~b(s(z), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3670, 233, 3648, 53, 3664])).
% 1.35/1.53 tff(3672,plain,
% 1.35/1.53 (r(s(z), s(s(z)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[481, 45, 34, 3671])).
% 1.35/1.53 tff(3673,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3674,plain,
% 1.35/1.53 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(3675,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[3674])).
% 1.35/1.53 tff(3676,plain,
% 1.35/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[3675, 3673])).
% 1.35/1.54 tff(3677,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(3678,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3677, 3676])).
% 1.35/1.54 tff(3679,plain,
% 1.35/1.54 (~b(s(s(z)), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3678, 233, 3648, 53, 3664])).
% 1.35/1.54 tff(3680,plain,
% 1.35/1.54 (r(s(s(z)), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[48, 45, 35, 3679])).
% 1.35/1.54 tff(3681,plain,
% 1.35/1.54 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3682,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3681])).
% 1.35/1.54 tff(3683,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[3682, 3084])).
% 1.35/1.54 tff(3684,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(3685,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3684, 3683])).
% 1.35/1.54 tff(3686,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3685, 108, 493, 3680, 3662, 3672])).
% 1.35/1.54 tff(3687,plain,((~r(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3688,plain,
% 1.35/1.54 (~r(z, s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3687, 649, 492, 53, 97])).
% 1.35/1.54 tff(3689,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[359, 3688, 3644])).
% 1.35/1.54 tff(3690,plain,((~b(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3691,plain,
% 1.35/1.54 (~b(s(s(z)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3690, 3641, 53, 79, 442])).
% 1.35/1.54 tff(3692,plain,
% 1.35/1.54 (r(s(s(z)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[374, 3691])).
% 1.35/1.54 tff(3693,plain,
% 1.35/1.54 (~r(z, elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1251, 3692, 3643, 3641])).
% 1.35/1.54 tff(3694,plain,
% 1.35/1.54 (~r(z, s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[703, 3692, 3643, 3641])).
% 1.35/1.54 tff(3695,plain,
% 1.35/1.54 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1726])).
% 1.35/1.54 tff(3696,plain,
% 1.35/1.54 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.35/1.54 inference(symmetry,[status(thm)],[3695])).
% 1.35/1.54 tff(3697,plain,
% 1.35/1.54 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3696])).
% 1.35/1.54 tff(3698,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.35/1.54 tff(3699,plain,
% 1.35/1.54 (r(s(s(s(z))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[340, 3698])).
% 1.35/1.54 tff(3700,plain,
% 1.35/1.54 (r(s(s(z)), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1814, 1053, 701])).
% 1.35/1.54 tff(3701,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.35/1.54 tff(3702,plain,
% 1.35/1.54 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1628])).
% 1.35/1.54 tff(3703,plain,
% 1.35/1.54 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.35/1.54 inference(symmetry,[status(thm)],[3702])).
% 1.35/1.54 tff(3704,plain,
% 1.35/1.54 ((~b(s(s(s(z))), z)) <=> (~b(s(s(s(z))), elem!1))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3703])).
% 1.35/1.54 tff(3705,plain,
% 1.35/1.54 (~b(s(s(s(z))), elem!1)),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3701, 3704])).
% 1.35/1.54 tff(3706,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[707, 3705])).
% 1.35/1.54 tff(3707,plain,((~(elem!1 = z)) | (~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3708,plain,
% 1.35/1.54 (~b(s(s(s(z))), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3707, 1741, 3701])).
% 1.35/1.54 tff(3709,plain,
% 1.35/1.54 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1628])).
% 1.35/1.54 tff(3710,plain,
% 1.35/1.54 (r(z, s(s(z)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[994, 3709])).
% 1.35/1.54 tff(3711,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[354, 3710])).
% 1.35/1.54 tff(3712,plain,((~r(elem!1, s(s(z)))) | r(z, s(s(z))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3713,plain,
% 1.35/1.54 (~r(elem!1, s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3712, 1741, 354])).
% 1.35/1.54 tff(3714,plain,
% 1.35/1.54 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1053])).
% 1.35/1.54 tff(3715,plain,
% 1.35/1.54 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.35/1.54 inference(symmetry,[status(thm)],[3714])).
% 1.35/1.54 tff(3716,plain,
% 1.35/1.54 (b(z, s(s(s(z))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[919, 3715])).
% 1.35/1.54 tff(3717,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[54, 3716])).
% 1.35/1.54 tff(3718,plain,((~(z = elem!1)) | b(z, s(s(s(z)))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3719,plain,
% 1.35/1.54 (~b(elem!1, s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3718, 1053, 54])).
% 1.35/1.54 tff(3720,plain,
% 1.35/1.54 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[1677])).
% 1.35/1.54 tff(3721,plain,
% 1.35/1.54 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.35/1.54 inference(symmetry,[status(thm)],[3720])).
% 1.35/1.54 tff(3722,plain,
% 1.35/1.54 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3721])).
% 1.35/1.54 tff(3723,plain,
% 1.35/1.54 (~b(s(s(z)), s(s(s(z))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[873, 3722])).
% 1.35/1.54 tff(3724,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[80, 3723])).
% 1.35/1.54 tff(3725,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(z)), s(s(s(z))))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3726,plain,
% 1.35/1.54 (~(s(s(z)) = elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3725, 3719, 80])).
% 1.35/1.54 tff(3727,plain,
% 1.35/1.54 (~(elem!1 = s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1697, 3726])).
% 1.35/1.54 tff(3728,plain,
% 1.35/1.54 (b(elem!1, s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1236, 3727, 3713])).
% 1.35/1.54 tff(3729,plain,
% 1.35/1.54 (b(s(s(s(z))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[834])).
% 1.35/1.54 tff(3730,plain,
% 1.35/1.54 (b(elem!1, s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.35/1.54 inference(symmetry,[status(thm)],[3729])).
% 1.35/1.54 tff(3731,plain,
% 1.35/1.54 (b(s(s(s(z))), s(s(z)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1009, 3730])).
% 1.35/1.54 tff(3732,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3698, 3731])).
% 1.35/1.54 tff(3733,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(s(z))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3734,plain,
% 1.35/1.54 (~(s(s(s(z))) = elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3733, 3728, 3698])).
% 1.35/1.54 tff(3735,plain,
% 1.35/1.54 (r(s(s(s(z))), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[843, 3734, 3708])).
% 1.35/1.54 tff(3736,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3737,plain,
% 1.35/1.54 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3738,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3737])).
% 1.35/1.54 tff(3739,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[3738, 3736])).
% 1.35/1.54 tff(3740,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(3741,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 1.35/1.54 tff(3742,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3741, 108, 1213, 862, 492, 1577])).
% 1.35/1.54 tff(3743,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3744,plain,
% 1.35/1.54 (~r(elem!1, s(s(s(elem!1))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3743, 3735, 3700, 3699])).
% 1.35/1.54 tff(3745,plain,
% 1.35/1.54 (~r(elem!1, s(s(s(z))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3744, 3697])).
% 1.35/1.54 tff(3746,plain,
% 1.35/1.54 (~(elem!1 = s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1051, 3734])).
% 1.35/1.54 tff(3747,plain,
% 1.35/1.54 (r(elem!1, s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[886, 3746, 3719])).
% 1.35/1.54 tff(3748,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3747, 3745])).
% 1.35/1.54 tff(3749,plain,((~(z = elem!1)) | b(s(s(s(z))), s(s(z))) | (~b(s(s(z)), s(s(s(z))))) | r(z, s(s(z))) | b(s(s(s(z))), z) | b(z, s(s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3750,plain,
% 1.35/1.54 (~(z = elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3749, 3694, 80, 54, 3642, 3640, 3692])).
% 1.35/1.54 tff(3751,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[934, 3750, 3693, 1027])).
% 1.35/1.54 tff(3752,plain,((~b(s(s(s(s(z)))), s(s(z)))) | b(z, elem!1) | (~b(s(s(z)), s(s(s(z))))) | b(z, s(s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3753,plain,
% 1.35/1.54 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3752, 3631, 80, 54, 53, 3539])).
% 1.35/1.54 tff(3754,plain,
% 1.35/1.54 (r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[462, 3753])).
% 1.35/1.54 tff(3755,plain,
% 1.35/1.54 (~b(z, s(s(s(s(s(z))))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3556, 3630, 53])).
% 1.35/1.54 tff(3756,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.35/1.54 tff(3757,plain,
% 1.35/1.54 (s(s(s(s(s(z))))) = z),
% 1.35/1.54 inference(symmetry,[status(thm)],[3756])).
% 1.35/1.54 tff(3758,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[514, 3757])).
% 1.35/1.54 tff(3759,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3760,assumption,(~r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.35/1.54 tff(3761,assumption,(~b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.35/1.54 tff(3762,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2864, 45, 3761, 3760, 3759])).
% 1.35/1.54 tff(3763,plain,(r(z, s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3764,plain,
% 1.35/1.54 (r(z, s(s(s(s(s(z))))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3763, 3755])).
% 1.35/1.54 tff(3765,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.35/1.54 tff(3766,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3618, 108, 97, 81, 1537, 3765])).
% 1.35/1.54 tff(3767,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3768,plain,
% 1.35/1.54 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3767, 3764, 81, 79])).
% 1.35/1.54 tff(3769,plain,
% 1.35/1.54 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[598, 3768])).
% 1.35/1.54 tff(3770,plain,
% 1.35/1.54 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3610, 284, 80, 680, 1547, 389])).
% 1.35/1.54 tff(3771,plain,
% 1.35/1.54 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[440, 3770])).
% 1.35/1.54 tff(3772,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3773,plain,
% 1.35/1.54 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3774,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3773])).
% 1.35/1.54 tff(3775,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[3774, 3772])).
% 1.35/1.54 tff(3776,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(3777,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 1.35/1.54 tff(3778,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3777, 233, 389, 284, 80, 3771])).
% 1.35/1.54 tff(3779,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3780,plain,
% 1.35/1.54 (~b(s(s(s(z))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3779, 3539, 80, 3754, 3769])).
% 1.35/1.54 tff(3781,plain,
% 1.35/1.54 (r(s(s(s(z))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[340, 3780])).
% 1.35/1.54 tff(3782,plain,
% 1.35/1.54 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[688, 3781, 81, 3754])).
% 1.35/1.54 tff(3783,plain,
% 1.35/1.54 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[440, 3782])).
% 1.35/1.54 tff(3784,plain,
% 1.35/1.54 (~r(s(s(z)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2552, 3781, 81, 3754])).
% 1.35/1.54 tff(3785,plain,
% 1.35/1.54 (b(s(s(z)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[374, 3784])).
% 1.35/1.54 tff(3786,plain,
% 1.35/1.54 (~r(z, s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3687, 3785, 53, 3781, 79])).
% 1.35/1.54 tff(3787,plain,
% 1.35/1.54 (b(z, s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[359, 3786])).
% 1.35/1.54 tff(3788,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2266, 233, 3787, 3785, 3783, 53])).
% 1.35/1.54 tff(3789,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3790,plain,
% 1.35/1.54 (~b(s(s(s(s(z)))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3789, 81, 80, 54])).
% 1.35/1.54 tff(3791,plain,
% 1.35/1.54 (r(s(s(s(s(z)))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3228, 3790])).
% 1.35/1.54 tff(3792,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3223, 108, 130, 97, 81, 3244])).
% 1.35/1.54 tff(3793,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3794,plain,
% 1.35/1.54 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3793, 81, 79, 3791])).
% 1.35/1.54 tff(3795,plain,
% 1.35/1.54 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[386, 3794])).
% 1.35/1.54 tff(3796,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3262, 108, 97, 247, 81, 3244])).
% 1.35/1.54 tff(3797,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3798,plain,
% 1.35/1.54 (~r(s(s(s(z))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3797, 81, 79, 3791])).
% 1.35/1.54 tff(3799,plain,
% 1.35/1.54 (b(s(s(s(z))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[244, 3798])).
% 1.35/1.54 tff(3800,plain,
% 1.35/1.54 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[638, 3799, 80, 3795])).
% 1.35/1.54 tff(3801,plain,
% 1.35/1.54 (r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[462, 3800])).
% 1.35/1.54 tff(3802,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3803,plain,
% 1.35/1.54 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3804,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3803])).
% 1.35/1.54 tff(3805,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[3804, 3802])).
% 1.35/1.54 tff(3806,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(3807,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3806, 3805])).
% 1.35/1.54 tff(3808,plain,
% 1.35/1.54 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3807, 233, 3795, 80, 3799])).
% 1.35/1.54 tff(3809,plain,
% 1.35/1.54 (r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[440, 3808])).
% 1.35/1.54 tff(3810,plain,
% 1.35/1.54 (~r(s(s(s(z))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[688, 3809, 81, 3801])).
% 1.35/1.54 tff(3811,plain,
% 1.35/1.54 (b(s(s(s(z))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[340, 3810])).
% 1.35/1.54 tff(3812,plain,
% 1.35/1.54 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3779, 3811, 80, 3795, 3801])).
% 1.35/1.54 tff(3813,plain,
% 1.35/1.54 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[598, 3812])).
% 1.35/1.54 tff(3814,plain,
% 1.35/1.54 (~r(s(s(z)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3354, 3801, 79, 3791])).
% 1.35/1.54 tff(3815,plain,
% 1.35/1.54 (b(s(s(z)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[374, 3814])).
% 1.35/1.54 tff(3816,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3817,plain,
% 1.35/1.54 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3818,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[3817])).
% 1.35/1.54 tff(3819,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[3818, 3816])).
% 1.35/1.54 tff(3820,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(3821,plain,
% 1.35/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 1.35/1.54 tff(3822,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3821, 233, 284, 649, 272, 3548])).
% 1.35/1.54 tff(3823,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3824,plain,
% 1.35/1.54 (~b(z, s(s(s(s(s(z))))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3823, 3811, 3799, 3815])).
% 1.35/1.54 tff(3825,plain,
% 1.35/1.54 (r(z, s(s(s(s(s(z))))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3763, 3824])).
% 1.35/1.54 tff(3826,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3767, 3825, 3813, 81, 79])).
% 1.35/1.54 tff(3827,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(3828,plain,
% 1.35/1.54 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3827, 80, 54])).
% 1.35/1.54 tff(3829,plain,
% 1.35/1.54 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[186, 3828])).
% 1.35/1.54 tff(3830,plain,
% 1.35/1.54 (~b(s(s(s(z))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3241, 2751, 204, 53])).
% 1.35/1.54 tff(3831,plain,
% 1.35/1.54 (r(s(s(s(z))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1090, 3830])).
% 1.35/1.54 tff(3832,plain,
% 1.35/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(3833,plain,
% 1.35/1.54 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3834,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3833])).
% 1.35/1.55 tff(3835,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3834, 3832])).
% 1.35/1.55 tff(3836,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3837,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3836, 3835])).
% 1.35/1.55 tff(3838,plain,
% 1.35/1.55 (~b(s(z), s(s(s(z))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3837, 233, 53, 204, 2751])).
% 1.35/1.55 tff(3839,plain,
% 1.35/1.55 (r(s(z), s(s(s(z))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[325, 3838])).
% 1.35/1.55 tff(3840,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3841,plain,
% 1.35/1.55 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3842,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3841])).
% 1.35/1.55 tff(3843,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3842, 3840])).
% 1.35/1.55 tff(3844,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3845,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3844, 3843])).
% 1.35/1.55 tff(3846,plain,
% 1.35/1.55 (~r(s(z), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3845, 108, 97, 3839, 3831])).
% 1.35/1.55 tff(3847,plain,
% 1.35/1.55 (b(s(z), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[260, 3846])).
% 1.35/1.55 tff(3848,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3849,plain,
% 1.35/1.55 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3850,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3849])).
% 1.35/1.55 tff(3851,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3850, 3848])).
% 1.35/1.55 tff(3852,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3853,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3852, 3851])).
% 1.35/1.55 tff(3854,plain,
% 1.35/1.55 (~r(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3853, 108, 97, 3839, 3831])).
% 1.35/1.55 tff(3855,plain,
% 1.35/1.55 (b(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[128, 3854])).
% 1.35/1.55 tff(3856,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3857,plain,
% 1.35/1.55 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3858,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3857])).
% 1.35/1.55 tff(3859,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3858, 3856])).
% 1.35/1.55 tff(3860,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3861,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3860, 3859])).
% 1.35/1.55 tff(3862,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3861, 233, 53, 2751, 388, 402])).
% 1.35/1.55 tff(3863,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(3864,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3863, 3855, 3847, 53])).
% 1.35/1.55 tff(3865,plain,((~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(3866,plain,
% 1.35/1.55 (~b(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3865, 3829, 79])).
% 1.35/1.55 tff(3867,plain,
% 1.35/1.55 (r(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3228, 3866])).
% 1.35/1.55 tff(3868,plain,
% 1.35/1.55 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3457, 1072, 204, 389])).
% 1.35/1.55 tff(3869,plain,
% 1.35/1.55 (~r(s(z), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1866, 1072, 80, 389])).
% 1.35/1.55 tff(3870,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1122, 3869, 3868])).
% 1.35/1.55 tff(3871,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(3872,plain,
% 1.35/1.55 (~b(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3871, 389, 80, 204])).
% 1.35/1.55 tff(3873,plain,
% 1.35/1.55 (r(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1090, 3872])).
% 1.35/1.55 tff(3874,plain,
% 1.35/1.55 (~b(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3865, 204, 97])).
% 1.35/1.55 tff(3875,plain,
% 1.35/1.55 (r(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3228, 3874])).
% 1.35/1.55 tff(3876,plain,
% 1.35/1.55 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[450, 389, 80, 204])).
% 1.35/1.55 tff(3877,plain,
% 1.35/1.55 (r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[462, 3876])).
% 1.35/1.55 tff(3878,plain,
% 1.35/1.55 (~r(s(s(z)), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3354, 3877, 97, 3875])).
% 1.35/1.55 tff(3879,plain,
% 1.35/1.55 (b(s(s(z)), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[374, 3878])).
% 1.35/1.55 tff(3880,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3881,plain,
% 1.35/1.55 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3882,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3881])).
% 1.35/1.55 tff(3883,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3882, 3880])).
% 1.35/1.55 tff(3884,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3885,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3884, 3883])).
% 1.35/1.55 tff(3886,plain,
% 1.35/1.55 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3885, 233, 389, 80, 204])).
% 1.35/1.55 tff(3887,plain,
% 1.35/1.55 (r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[440, 3886])).
% 1.35/1.55 tff(3888,plain,
% 1.35/1.55 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3779, 284, 80, 389, 680])).
% 1.35/1.55 tff(3889,plain,
% 1.35/1.55 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[598, 3888])).
% 1.35/1.55 tff(3890,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3891,plain,
% 1.35/1.55 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3892,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3891])).
% 1.35/1.55 tff(3893,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3892, 3890])).
% 1.35/1.55 tff(3894,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3895,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 1.35/1.55 tff(3896,plain,
% 1.35/1.55 (~r(s(s(s(s(s(z))))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3895, 108, 97, 92, 3889])).
% 1.35/1.55 tff(3897,plain,
% 1.35/1.55 (b(s(s(s(s(s(z))))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[517, 45, 514, 3896])).
% 1.35/1.55 tff(3898,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3899,plain,
% 1.35/1.55 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3900,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3899])).
% 1.35/1.55 tff(3901,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3900, 3898])).
% 1.35/1.55 tff(3902,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3903,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3902, 3901])).
% 1.35/1.55 tff(3904,plain,
% 1.35/1.55 (~r(z, s(s(s(s(s(z))))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3903, 108, 97, 92, 3889])).
% 1.35/1.55 tff(3905,plain,
% 1.35/1.55 (b(z, s(s(s(s(s(z))))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3763, 3904])).
% 1.35/1.55 tff(3906,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3907,plain,
% 1.35/1.55 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3908,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3907])).
% 1.35/1.55 tff(3909,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[3908, 3906])).
% 1.35/1.55 tff(3910,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(3911,plain,
% 1.35/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[3910, 3909])).
% 1.35/1.55 tff(3912,plain,
% 1.35/1.55 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3911, 233, 649, 3905, 3897])).
% 1.35/1.55 tff(3913,plain,
% 1.35/1.55 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[535, 45, 532, 3912])).
% 1.35/1.55 tff(3914,plain,
% 1.35/1.55 (~b(s(s(s(z))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3823, 3905, 284, 649])).
% 1.35/1.55 tff(3915,plain,
% 1.35/1.55 (r(s(s(s(z))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[244, 3914])).
% 1.35/1.55 tff(3916,plain,
% 1.35/1.55 (~r(s(z), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[255, 3915, 97, 92])).
% 1.35/1.55 tff(3917,plain,
% 1.35/1.55 (b(s(z), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[260, 3916])).
% 1.35/1.55 tff(3918,plain,
% 1.35/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(3919,plain,
% 1.35/1.55 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3920,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[3919])).
% 1.35/1.56 tff(3921,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[3920, 3918])).
% 1.35/1.56 tff(3922,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(3923,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[3922, 3921])).
% 1.35/1.56 tff(3924,plain,
% 1.35/1.56 (~b(s(z), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3923, 233, 649, 3917, 3905])).
% 1.35/1.56 tff(3925,plain,
% 1.35/1.56 (r(s(z), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[2414, 3924])).
% 1.35/1.56 tff(3926,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3927,plain,
% 1.35/1.56 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3928,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[3927])).
% 1.35/1.56 tff(3929,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[3928, 3926])).
% 1.35/1.56 tff(3930,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(3931,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[3930, 3929])).
% 1.35/1.56 tff(3932,plain,
% 1.35/1.56 (~b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3931, 233, 3917, 3905, 3897])).
% 1.35/1.56 tff(3933,plain,
% 1.35/1.56 (b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[556, 91])).
% 1.35/1.56 tff(3934,plain,
% 1.35/1.56 (r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3933, 3932])).
% 1.35/1.56 tff(3935,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3936,plain,
% 1.35/1.56 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3937,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[3936])).
% 1.35/1.56 tff(3938,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[3937, 3935])).
% 1.35/1.56 tff(3939,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(3940,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[3939, 3938])).
% 1.35/1.56 tff(3941,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3940, 108, 491, 3934, 3925, 3913])).
% 1.35/1.56 tff(3942,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(3943,plain,
% 1.35/1.56 (~b(s(s(s(z))), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3942, 3887, 3879, 97, 3873, 80, 389, 3877])).
% 1.35/1.56 tff(3944,plain,
% 1.35/1.56 (r(s(s(s(z))), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[340, 3943])).
% 1.35/1.56 tff(3945,plain,
% 1.35/1.56 (~r(z, s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[501, 3944, 97, 3887])).
% 1.35/1.56 tff(3946,plain,
% 1.35/1.56 (b(z, s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[359, 3945])).
% 1.35/1.56 tff(3947,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3948,plain,
% 1.35/1.56 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3949,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[3948])).
% 1.35/1.56 tff(3950,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[3949, 3947])).
% 1.35/1.56 tff(3951,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(3952,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[3951, 3950])).
% 1.35/1.56 tff(3953,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3952, 233, 80, 706, 649, 272])).
% 1.35/1.56 tff(3954,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(3955,plain,
% 1.35/1.56 (~b(s(s(s(z))), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3954, 3946, 80, 3879])).
% 1.35/1.56 tff(3956,plain,
% 1.35/1.56 (r(s(s(s(z))), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[244, 3955])).
% 1.35/1.56 tff(3957,plain,
% 1.35/1.56 (~r(s(z), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[255, 3956, 97, 3873])).
% 1.35/1.56 tff(3958,plain,
% 1.35/1.56 (b(s(z), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[260, 3957])).
% 1.35/1.56 tff(3959,plain,
% 1.35/1.56 (~b(s(z), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[2358, 233, 3946, 3879, 3958])).
% 1.35/1.56 tff(3960,plain,
% 1.35/1.56 (r(s(z), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[2414, 3959])).
% 1.35/1.56 tff(3961,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3962,plain,
% 1.35/1.56 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3963,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[3962])).
% 1.35/1.56 tff(3964,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[3963, 3961])).
% 1.35/1.56 tff(3965,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(3966,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[3965, 3964])).
% 1.35/1.56 tff(3967,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3966, 108, 3944, 3887, 3873, 3960])).
% 1.35/1.56 tff(3968,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(3969,plain,
% 1.35/1.56 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3968, 80, 79, 3829])).
% 1.35/1.56 tff(3970,plain,
% 1.35/1.56 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[386, 3969])).
% 1.35/1.56 tff(3971,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3285, 108, 130, 97, 247, 3244])).
% 1.35/1.56 tff(3972,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(3973,plain,
% 1.35/1.56 (~r(s(s(s(z))), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3972, 3970, 79, 3867])).
% 1.35/1.56 tff(3974,plain,
% 1.35/1.56 (b(s(s(s(z))), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[244, 3973])).
% 1.35/1.56 tff(3975,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3976,plain,
% 1.35/1.56 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3977,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[3976])).
% 1.35/1.56 tff(3978,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[3977, 3975])).
% 1.35/1.56 tff(3979,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(3980,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[3979, 3978])).
% 1.35/1.56 tff(3981,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3980, 108, 130, 97, 3244, 92])).
% 1.35/1.56 tff(3982,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(3983,plain,
% 1.35/1.56 (~r(s(s(s(z))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3982, 3970, 79, 3867])).
% 1.35/1.56 tff(3984,plain,
% 1.35/1.56 (b(s(s(s(z))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1090, 3983])).
% 1.35/1.56 tff(3985,plain,
% 1.35/1.56 (~r(s(s(s(z))), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3335, 3970, 79, 3867])).
% 1.35/1.56 tff(3986,plain,
% 1.35/1.56 (b(s(s(s(z))), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[340, 3985])).
% 1.35/1.56 tff(3987,plain,
% 1.35/1.56 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3364, 442, 204, 284])).
% 1.35/1.56 tff(3988,plain,
% 1.35/1.56 (r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[440, 3987])).
% 1.35/1.56 tff(3989,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3990,plain,
% 1.35/1.56 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(3991,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[3990])).
% 1.35/1.56 tff(3992,plain,
% 1.35/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[3991, 3989])).
% 1.35/1.56 tff(3993,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(3994,plain,
% 1.35/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[3993, 3992])).
% 1.35/1.56 tff(3995,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3994, 233, 442, 272, 1930, 204])).
% 1.35/1.56 tff(3996,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(3997,plain,
% 1.35/1.56 (~b(z, s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3996, 442, 204, 272])).
% 1.35/1.56 tff(3998,plain,
% 1.35/1.56 (r(z, s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[222, 3997])).
% 1.35/1.56 tff(3999,plain,
% 1.35/1.56 (~b(s(s(z)), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[2398, 442, 204, 284])).
% 1.35/1.56 tff(4000,plain,
% 1.35/1.56 (r(s(s(z)), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[374, 3999])).
% 1.35/1.56 tff(4001,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(4002,plain,
% 1.35/1.56 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(4003,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[4002])).
% 1.35/1.56 tff(4004,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[4003, 4001])).
% 1.35/1.56 tff(4005,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(4006,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[4005, 4004])).
% 1.35/1.56 tff(4007,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[4006, 108, 701, 491, 978, 3244])).
% 1.35/1.57 tff(4008,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4009,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4008, 4000, 3998, 3244, 3988])).
% 1.35/1.57 tff(4010,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4011,plain,
% 1.35/1.57 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4010, 3867, 3829, 3986, 3974])).
% 1.35/1.57 tff(4012,plain,
% 1.35/1.57 (r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[462, 4011])).
% 1.35/1.57 tff(4013,plain,
% 1.35/1.57 (~b(z, s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[3433, 3974, 79, 3829, 3970])).
% 1.35/1.57 tff(4014,plain,
% 1.35/1.57 (r(z, s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[359, 4013])).
% 1.35/1.57 tff(4015,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4016,plain,
% 1.35/1.57 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4017,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4016])).
% 1.35/1.57 tff(4018,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4017, 4015])).
% 1.35/1.57 tff(4019,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4020,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[4019, 4018])).
% 1.35/1.57 tff(4021,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4020, 108, 493, 680, 3244, 2051])).
% 1.35/1.57 tff(4022,plain,((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4023,plain,
% 1.35/1.57 (~r(s(s(z)), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4022, 4014, 4012, 3867])).
% 1.35/1.57 tff(4024,plain,
% 1.35/1.57 (b(s(s(z)), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[50, 4023])).
% 1.35/1.57 tff(4025,plain,
% 1.35/1.57 (~b(s(z), s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[2986, 4024, 80, 3984])).
% 1.35/1.57 tff(4026,plain,
% 1.35/1.57 (r(s(z), s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[2414, 4025])).
% 1.35/1.57 tff(4027,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4028,plain,
% 1.35/1.57 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4029,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4028])).
% 1.35/1.57 tff(4030,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4029, 4027])).
% 1.35/1.57 tff(4031,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4032,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[4031, 4030])).
% 1.35/1.57 tff(4033,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4032, 108, 97, 3244, 246, 188])).
% 1.35/1.57 tff(4034,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4035,plain,
% 1.35/1.57 (~r(s(z), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4034, 188, 3244, 97])).
% 1.35/1.57 tff(4036,plain,
% 1.35/1.57 (b(s(z), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[260, 4035])).
% 1.35/1.57 tff(4037,plain,
% 1.35/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4038,plain,
% 1.35/1.57 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4039,plain,
% 1.35/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4038])).
% 1.35/1.57 tff(4040,plain,
% 1.35/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4039, 4037])).
% 1.35/1.57 tff(4041,plain,
% 1.35/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4042,plain,
% 1.35/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[4041, 4040])).
% 1.35/1.57 tff(4043,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4042, 233, 272, 1072, 388, 402])).
% 1.35/1.57 tff(4044,plain,((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4045,plain,
% 1.35/1.57 (~b(z, s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4044, 4036, 1072, 272])).
% 1.35/1.57 tff(4046,plain,
% 1.35/1.57 (r(z, s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[128, 4045])).
% 1.35/1.57 tff(4047,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4048,plain,
% 1.35/1.57 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4049,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4048])).
% 1.35/1.57 tff(4050,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4049, 4047])).
% 1.35/1.57 tff(4051,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4052,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[4051, 4050])).
% 1.35/1.57 tff(4053,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4052, 108, 3244, 4046, 188, 2401])).
% 1.35/1.57 tff(4054,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4055,plain,
% 1.35/1.57 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4054, 3867, 4026, 3984, 3974, 79])).
% 1.35/1.57 tff(4056,plain,
% 1.35/1.57 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[200, 45, 4055, 69])).
% 1.35/1.57 tff(4057,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4058,plain,
% 1.35/1.57 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4059,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4058])).
% 1.35/1.57 tff(4060,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4059, 4057])).
% 1.35/1.57 tff(4061,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4062,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[4061, 4060])).
% 1.35/1.57 tff(4063,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4062, 108, 493, 680, 491, 3244])).
% 1.35/1.57 tff(4064,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4065,plain,
% 1.35/1.57 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4064, 4014, 4012, 3867])).
% 1.35/1.57 tff(4066,plain,
% 1.35/1.57 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[440, 4065])).
% 1.35/1.57 tff(4067,plain,
% 1.35/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4068,plain,
% 1.35/1.57 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4069,plain,
% 1.35/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4068])).
% 1.35/1.57 tff(4070,plain,
% 1.35/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4069, 4067])).
% 1.35/1.57 tff(4071,plain,
% 1.35/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4072,plain,
% 1.35/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[4071, 4070])).
% 1.35/1.57 tff(4073,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4072, 233, 3986, 4066, 3829, 4056])).
% 1.35/1.57 tff(4074,plain,((~b(s(s(z)), s(s(s(z))))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4075,plain,
% 1.35/1.57 (~b(s(s(z)), s(s(s(z))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4074, 54])).
% 1.35/1.57 tff(4076,plain,
% 1.35/1.57 (r(s(s(z)), s(s(s(z))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[2228, 4075])).
% 1.35/1.57 tff(4077,plain,
% 1.35/1.57 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[3587, 53, 2240])).
% 1.35/1.57 tff(4078,plain,
% 1.35/1.57 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[3865, 53, 97])).
% 1.35/1.57 tff(4079,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[186, 4078, 4077])).
% 1.35/1.57 tff(4080,plain,((~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(4081,plain,
% 1.35/1.57 (~b(s(s(s(s(z)))), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4080, 79, 4076])).
% 1.35/1.57 tff(4082,plain,
% 1.35/1.57 (r(s(s(s(s(z)))), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[3228, 4081])).
% 1.35/1.57 tff(4083,plain,
% 1.35/1.57 (~b(s(s(s(s(z)))), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4080, 97, 2240])).
% 1.35/1.57 tff(4084,plain,
% 1.35/1.57 (r(s(s(s(s(z)))), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[3228, 4083])).
% 1.35/1.57 tff(4085,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4086,plain,
% 1.35/1.57 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4087,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4086])).
% 1.35/1.57 tff(4088,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4087, 4085])).
% 1.35/1.57 tff(4089,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4090,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 1.35/1.57 tff(4091,plain,
% 1.35/1.57 (~r(s(s(z)), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[4090, 108, 492, 2240, 97])).
% 1.35/1.57 tff(4092,plain,
% 1.35/1.57 (b(s(s(z)), z)),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[374, 4091])).
% 1.35/1.57 tff(4093,plain,
% 1.35/1.57 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.35/1.57 inference(commutativity,[status(thm)],[])).
% 1.35/1.57 tff(4094,plain,
% 1.35/1.57 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.35/1.57 inference(symmetry,[status(thm)],[4093])).
% 1.35/1.57 tff(4095,plain,
% 1.35/1.57 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4094])).
% 1.35/1.57 tff(4096,plain,
% 1.35/1.57 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[532, 4095])).
% 1.35/1.57 tff(4097,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4098,plain,
% 1.35/1.57 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(4099,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[4098])).
% 1.35/1.57 tff(4100,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[4099, 4097])).
% 1.35/1.57 tff(4101,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(4102,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4101, 4100])).
% 1.35/1.58 tff(4103,plain,
% 1.35/1.58 (~r(s(s(s(s(s(z))))), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4102, 108, 492, 97, 1537])).
% 1.35/1.58 tff(4104,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[517, 45, 514, 4103])).
% 1.35/1.58 tff(4105,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4106,plain,
% 1.35/1.58 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4107,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[4106])).
% 1.35/1.58 tff(4108,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[4107, 4105])).
% 1.35/1.58 tff(4109,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(4110,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 1.35/1.58 tff(4111,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4110, 108, 97, 247, 1537, 3765])).
% 1.35/1.58 tff(4112,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(4113,plain,
% 1.35/1.58 (~r(z, s(s(s(s(s(z))))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4112, 1537, 247, 97])).
% 1.35/1.58 tff(4114,plain,
% 1.35/1.58 (b(z, s(s(s(s(s(z))))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3763, 4113])).
% 1.35/1.58 tff(4115,plain,
% 1.35/1.58 (~r(z, s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[2248, 492, 97, 2240])).
% 1.35/1.58 tff(4116,plain,
% 1.35/1.58 (b(z, s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[359, 4115])).
% 1.35/1.58 tff(4117,plain,
% 1.35/1.58 (~r(s(z), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[2360, 247, 97, 2240, 4116, 4092])).
% 1.35/1.58 tff(4118,plain,
% 1.35/1.58 (b(s(z), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[325, 4117])).
% 1.35/1.58 tff(4119,plain,
% 1.35/1.58 (~r(s(s(s(z))), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3797, 81, 97, 4084])).
% 1.35/1.58 tff(4120,plain,
% 1.35/1.58 (b(s(s(s(z))), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[244, 4119])).
% 1.35/1.58 tff(4121,plain,
% 1.35/1.58 (~r(s(z), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3005, 2337, 81, 97])).
% 1.35/1.58 tff(4122,plain,
% 1.35/1.58 (b(s(z), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[260, 4121])).
% 1.35/1.58 tff(4123,plain,
% 1.35/1.58 (~b(s(z), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[2358, 233, 4116, 4092, 4122])).
% 1.35/1.58 tff(4124,plain,
% 1.35/1.58 (r(s(z), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[2414, 4123])).
% 1.35/1.58 tff(4125,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4126,plain,
% 1.35/1.58 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4127,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[4126])).
% 1.35/1.58 tff(4128,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[4127, 4125])).
% 1.35/1.58 tff(4129,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(4130,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4129, 4128])).
% 1.35/1.58 tff(4131,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4130, 108, 492, 2240, 2337, 4124])).
% 1.35/1.58 tff(4132,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(4133,plain,
% 1.35/1.58 (~r(s(z), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4132, 81, 2240, 492, 97])).
% 1.35/1.58 tff(4134,plain,
% 1.35/1.58 (b(s(z), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[325, 4133])).
% 1.35/1.58 tff(4135,plain,
% 1.35/1.58 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3335, 492, 97, 4084])).
% 1.35/1.58 tff(4136,plain,
% 1.35/1.58 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[386, 4135])).
% 1.35/1.58 tff(4137,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4138,plain,
% 1.35/1.58 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4139,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[4138])).
% 1.35/1.58 tff(4140,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[4139, 4137])).
% 1.35/1.58 tff(4141,plain,
% 1.35/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(4142,plain,
% 1.35/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 1.35/1.58 tff(4143,plain,
% 1.35/1.58 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4142, 233, 4136, 4120, 4134])).
% 1.35/1.58 tff(4144,plain,
% 1.35/1.58 (r(s(z), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1122, 4143])).
% 1.35/1.58 tff(4145,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4146,plain,
% 1.35/1.58 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4147,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[4146])).
% 1.35/1.58 tff(4148,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[4147, 4145])).
% 1.35/1.58 tff(4149,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(4150,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4149, 4148])).
% 1.35/1.58 tff(4151,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4150, 108, 81, 3244, 92, 52])).
% 1.35/1.58 tff(4152,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(4153,plain,
% 1.35/1.58 (~r(s(s(s(z))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4152, 4144, 4084, 81])).
% 1.35/1.58 tff(4154,plain,
% 1.35/1.58 (b(s(s(s(z))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1090, 4153])).
% 1.35/1.58 tff(4155,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4156,plain,
% 1.35/1.58 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4157,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[4156])).
% 1.35/1.58 tff(4158,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[4157, 4155])).
% 1.35/1.58 tff(4159,plain,
% 1.35/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(4160,plain,
% 1.35/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4159, 4158])).
% 1.35/1.58 tff(4161,plain,
% 1.35/1.58 (~b(s(s(s(s(z)))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4160, 233, 4136, 4120, 4134])).
% 1.35/1.58 tff(4162,plain,
% 1.35/1.58 (r(s(s(s(s(z)))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[200, 45, 4161, 69])).
% 1.35/1.58 tff(4163,plain,
% 1.35/1.58 (~r(s(z), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4034, 4162, 4084, 97])).
% 1.35/1.58 tff(4164,plain,
% 1.35/1.58 (b(s(z), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[260, 4163])).
% 1.35/1.58 tff(4165,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4166,plain,
% 1.35/1.58 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4167,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[4166])).
% 1.35/1.58 tff(4168,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[4167, 4165])).
% 1.35/1.58 tff(4169,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(4170,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 1.35/1.58 tff(4171,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4170, 108, 3244, 52, 98, 188])).
% 1.35/1.58 tff(4172,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(4173,plain,
% 1.35/1.58 (~r(z, s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4172, 4162, 4084, 4144])).
% 1.35/1.58 tff(4174,plain,
% 1.35/1.58 (b(z, s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[128, 4173])).
% 1.35/1.58 tff(4175,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4044, 4174, 4164, 4154, 4120])).
% 1.35/1.58 tff(4176,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(4177,plain,
% 1.35/1.58 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4176, 492, 2240, 97])).
% 1.35/1.58 tff(4178,plain,
% 1.35/1.58 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[186, 4177])).
% 1.35/1.58 tff(4179,plain,
% 1.35/1.58 (~b(s(s(s(s(z)))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[2368, 233, 4136, 4178, 4118])).
% 1.35/1.58 tff(4180,plain,
% 1.35/1.58 (r(s(s(s(s(z)))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[200, 45, 4179, 69])).
% 1.35/1.58 tff(4181,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4182,plain,
% 1.35/1.58 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4183,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[4182])).
% 1.35/1.58 tff(4184,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[4183, 4181])).
% 1.35/1.58 tff(4185,plain,
% 1.35/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(4186,plain,
% 1.35/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 1.35/1.58 tff(4187,plain,
% 1.35/1.58 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4186, 233, 4136, 4178, 4118])).
% 1.35/1.58 tff(4188,plain,
% 1.35/1.58 (r(s(z), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1122, 4187])).
% 1.35/1.58 tff(4189,plain,
% 1.35/1.58 (~r(z, s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4172, 4180, 4084, 4188])).
% 1.35/1.58 tff(4190,plain,
% 1.35/1.58 (b(z, s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[128, 4189])).
% 1.35/1.58 tff(4191,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4192,plain,
% 1.35/1.58 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(4193,plain,
% 1.35/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4192])).
% 1.35/1.59 tff(4194,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[4193, 4191])).
% 1.35/1.59 tff(4195,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4196,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4195, 4194])).
% 1.35/1.59 tff(4197,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4196, 233, 388, 285, 504, 3548])).
% 1.35/1.59 tff(4198,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.59 tff(4199,plain,
% 1.35/1.59 (~b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4198, 4114, 4190, 4118])).
% 1.35/1.59 tff(4200,plain,
% 1.35/1.59 (r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[3933, 4199])).
% 1.35/1.59 tff(4201,plain,
% 1.35/1.59 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[2374, 108, 4188, 4200, 4180])).
% 1.35/1.59 tff(4202,plain,
% 1.35/1.59 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[579, 45, 576, 4201])).
% 1.35/1.59 tff(4203,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4204,plain,
% 1.35/1.59 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4205,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4204])).
% 1.35/1.59 tff(4206,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[4205, 4203])).
% 1.35/1.59 tff(4207,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4208,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4207, 4206])).
% 1.35/1.59 tff(4209,plain,
% 1.35/1.59 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4208, 108, 4188, 4200, 4180])).
% 1.35/1.59 tff(4210,plain,
% 1.35/1.59 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[745, 4209])).
% 1.35/1.59 tff(4211,plain,
% 1.35/1.59 (~r(s(z), z)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4034, 4180, 4084, 97])).
% 1.35/1.59 tff(4212,plain,
% 1.35/1.59 (b(s(z), z)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[260, 4211])).
% 1.35/1.59 tff(4213,plain,
% 1.35/1.59 (~b(s(z), s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[2358, 233, 4116, 4092, 4212])).
% 1.35/1.59 tff(4214,plain,
% 1.35/1.59 (r(s(z), s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[2414, 4213])).
% 1.35/1.59 tff(4215,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4216,plain,
% 1.35/1.59 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4217,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4216])).
% 1.35/1.59 tff(4218,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.35/1.59 inference(transitivity,[status(thm)],[4217, 4215])).
% 1.35/1.59 tff(4219,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4220,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), z))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4219, 4218])).
% 1.35/1.59 tff(4221,plain,
% 1.35/1.59 (~b(s(s(z)), s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4220, 233, 4116, 4092, 4212])).
% 1.35/1.59 tff(4222,plain,
% 1.35/1.59 (r(s(s(z)), s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[50, 4221])).
% 1.35/1.59 tff(4223,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4224,plain,
% 1.35/1.59 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4225,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4224])).
% 1.35/1.59 tff(4226,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[4225, 4223])).
% 1.35/1.59 tff(4227,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4228,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4227, 4226])).
% 1.35/1.59 tff(4229,plain,
% 1.35/1.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4228, 108, 4222, 4180, 4214])).
% 1.35/1.59 tff(4230,plain,
% 1.35/1.59 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[440, 4229])).
% 1.35/1.59 tff(4231,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4232,plain,
% 1.35/1.59 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4233,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4232])).
% 1.35/1.59 tff(4234,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[4233, 4231])).
% 1.35/1.59 tff(4235,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4236,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4235, 4234])).
% 1.35/1.59 tff(4237,plain,
% 1.35/1.59 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4236, 233, 4230, 4210, 4202, 4114, 4104])).
% 1.35/1.59 tff(4238,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4239,plain,
% 1.35/1.59 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4240,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4239])).
% 1.35/1.59 tff(4241,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[4240, 4238])).
% 1.35/1.59 tff(4242,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4243,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4242, 4241])).
% 1.35/1.59 tff(4244,plain,
% 1.35/1.59 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4243, 108, 492, 2240, 1537])).
% 1.35/1.59 tff(4245,plain,
% 1.35/1.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4246,plain,
% 1.35/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4247,plain,
% 1.35/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4246, 4245])).
% 1.35/1.59 tff(4248,plain,
% 1.35/1.59 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4247, 45, 4244])).
% 1.35/1.59 tff(4249,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4248, 4237, 4096])).
% 1.35/1.59 tff(4250,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.59 tff(4251,plain,
% 1.35/1.59 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4250, 247, 2240, 97, 492])).
% 1.35/1.59 tff(4252,plain,
% 1.35/1.59 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[598, 4251])).
% 1.35/1.59 tff(4253,plain,
% 1.35/1.59 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[2409, 4214, 2240, 4188])).
% 1.35/1.59 tff(4254,plain,
% 1.35/1.59 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[462, 4253])).
% 1.35/1.59 tff(4255,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4256,plain,
% 1.35/1.59 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4257,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4256])).
% 1.35/1.59 tff(4258,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[4257, 4255])).
% 1.35/1.59 tff(4259,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(4260,plain,
% 1.35/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[4259, 4258])).
% 1.35/1.59 tff(4261,plain,
% 1.35/1.59 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4260, 233, 4136, 4254, 4230, 4178, 4252])).
% 1.35/1.59 tff(4262,plain,
% 1.35/1.59 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[579, 45, 576, 4261])).
% 1.35/1.59 tff(4263,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4264,plain,
% 1.35/1.59 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(4265,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[4264])).
% 1.35/1.59 tff(4266,plain,
% 1.35/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[4265, 4263])).
% 1.45/1.60 tff(4267,plain,
% 1.45/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4268,plain,
% 1.45/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4267, 4266])).
% 1.45/1.60 tff(4269,plain,
% 1.45/1.60 (~b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4268, 233, 4178, 4252, 4118])).
% 1.45/1.60 tff(4270,plain,
% 1.45/1.60 (r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[3933, 4269])).
% 1.45/1.60 tff(4271,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2374, 108, 4188, 4270, 4180, 4262])).
% 1.45/1.60 tff(4272,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4273,plain,
% 1.45/1.60 (~r(s(s(s(z))), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4272, 492, 97, 2240])).
% 1.45/1.60 tff(4274,plain,
% 1.45/1.60 (b(s(s(s(z))), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[244, 4273])).
% 1.45/1.60 tff(4275,plain,
% 1.45/1.60 (r(s(z), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2414, 3297])).
% 1.45/1.60 tff(4276,plain,
% 1.45/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4277,plain,
% 1.45/1.60 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4278,plain,
% 1.45/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[4277])).
% 1.45/1.60 tff(4279,plain,
% 1.45/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[4278, 4276])).
% 1.45/1.60 tff(4280,plain,
% 1.45/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4281,plain,
% 1.45/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4280, 4279])).
% 1.45/1.60 tff(4282,plain,
% 1.45/1.60 (~b(s(z), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4281, 233, 706, 272, 402])).
% 1.45/1.60 tff(4283,plain,
% 1.45/1.60 (r(s(z), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[325, 4282])).
% 1.45/1.60 tff(4284,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4285,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4284, 4125])).
% 1.45/1.60 tff(4286,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4285, 108, 492, 2240, 4283, 4275])).
% 1.45/1.60 tff(4287,plain,((~b(s(z), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4288,plain,
% 1.45/1.60 (~b(s(z), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4287, 492, 2240, 4116, 4274, 4092])).
% 1.45/1.60 tff(4289,plain,
% 1.45/1.60 (r(s(z), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[260, 4288])).
% 1.45/1.60 tff(4290,plain,
% 1.45/1.60 (~r(s(s(s(s(z)))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4034, 4289, 4084, 97])).
% 1.45/1.60 tff(4291,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.45/1.60 tff(4292,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[200, 45, 798, 4291, 69])).
% 1.45/1.60 tff(4293,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4294,plain,
% 1.45/1.60 (b(s(s(s(s(z)))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4293, 4290])).
% 1.45/1.60 tff(4295,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2809, 108, 492, 97, 2337, 246])).
% 1.45/1.60 tff(4296,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4297,plain,
% 1.45/1.60 (~r(s(z), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4296, 4289, 97, 492])).
% 1.45/1.60 tff(4298,plain,
% 1.45/1.60 (b(s(z), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[325, 4297])).
% 1.45/1.60 tff(4299,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4160, 233, 4136, 4274, 4298, 4294])).
% 1.45/1.60 tff(4300,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4301,plain,
% 1.45/1.60 (~r(s(s(s(z))), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4300, 79, 4076])).
% 1.45/1.60 tff(4302,plain,
% 1.45/1.60 (b(s(s(s(z))), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[340, 4301])).
% 1.45/1.60 tff(4303,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.45/1.60 tff(4304,plain,
% 1.45/1.60 (r(s(s(z)), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[374, 368])).
% 1.45/1.60 tff(4305,plain,
% 1.45/1.60 (r(s(s(z)), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2228, 4303])).
% 1.45/1.60 tff(4306,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.45/1.60 tff(4307,plain,
% 1.45/1.60 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[386, 4306])).
% 1.45/1.60 tff(4308,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4309,plain,
% 1.45/1.60 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4310,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[4309])).
% 1.45/1.60 tff(4311,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[4310, 4308])).
% 1.45/1.60 tff(4312,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4313,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4312, 4311])).
% 1.45/1.60 tff(4314,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4313, 108, 130, 862, 2240, 491])).
% 1.45/1.60 tff(4315,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4316,plain,
% 1.45/1.60 (~r(s(s(s(z))), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4315, 4307, 4305, 491])).
% 1.45/1.60 tff(4317,plain,
% 1.45/1.60 (~r(s(s(s(z))), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2586, 4307, 4305, 491])).
% 1.45/1.60 tff(4318,plain,
% 1.45/1.60 (b(s(s(s(z))), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[244, 4317])).
% 1.45/1.60 tff(4319,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4320,plain,
% 1.45/1.60 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4321,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[4320])).
% 1.45/1.60 tff(4322,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[4321, 4319])).
% 1.45/1.60 tff(4323,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4324,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4323, 4322])).
% 1.45/1.60 tff(4325,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4324, 108, 130, 2240, 491, 92])).
% 1.45/1.60 tff(4326,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4327,plain,
% 1.45/1.60 (~r(s(s(s(z))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4326, 4307, 4305, 491])).
% 1.45/1.60 tff(4328,plain,
% 1.45/1.60 (b(s(s(s(z))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1090, 4327])).
% 1.45/1.60 tff(4329,plain,
% 1.45/1.60 (~r(s(z), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1894, 4328, 284, 4307, 491])).
% 1.45/1.60 tff(4330,plain,
% 1.45/1.60 (b(s(z), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1122, 4329])).
% 1.45/1.60 tff(4331,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4332,plain,
% 1.45/1.60 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4333,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[4332])).
% 1.45/1.60 tff(4334,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[4333, 4331])).
% 1.45/1.60 tff(4335,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4336,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4335, 4334])).
% 1.45/1.60 tff(4337,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4336, 108, 130, 2240, 491, 2849])).
% 1.45/1.60 tff(4338,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4339,plain,
% 1.45/1.60 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4338, 4307, 4305, 491])).
% 1.45/1.60 tff(4340,plain,
% 1.45/1.60 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[759, 4339])).
% 1.45/1.60 tff(4341,plain,
% 1.45/1.60 (~r(s(s(s(z))), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4315, 130, 4305, 491])).
% 1.45/1.60 tff(4342,plain,
% 1.45/1.60 (b(s(s(s(z))), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[843, 1049, 4341])).
% 1.45/1.60 tff(4343,plain,
% 1.45/1.60 (~r(s(s(s(z))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4326, 130, 4305, 491])).
% 1.45/1.60 tff(4344,plain,
% 1.45/1.60 (b(s(s(s(z))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1090, 4343])).
% 1.45/1.60 tff(4345,plain,
% 1.45/1.60 (~r(s(s(s(z))), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2586, 130, 4305, 491])).
% 1.45/1.60 tff(4346,plain,
% 1.45/1.60 (b(s(s(s(z))), z)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[244, 4345])).
% 1.45/1.60 tff(4347,plain,
% 1.45/1.60 (b(z, elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[934, 2848, 717])).
% 1.45/1.60 tff(4348,plain,
% 1.45/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4349,plain,
% 1.45/1.60 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4350,plain,
% 1.45/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[4349])).
% 1.45/1.60 tff(4351,plain,
% 1.45/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)))),
% 1.45/1.60 inference(transitivity,[status(thm)],[4350, 4348])).
% 1.45/1.60 tff(4352,plain,
% 1.45/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4353,plain,
% 1.45/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4352, 4351])).
% 1.45/1.60 tff(4354,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4353, 233, 921, 1009, 707, 272])).
% 1.45/1.60 tff(4355,plain,((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(4356,plain,
% 1.45/1.60 (~b(elem!1, s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4355, 4347, 707, 4346])).
% 1.45/1.60 tff(4357,plain,
% 1.45/1.60 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2598, 130, 4305, 491])).
% 1.45/1.60 tff(4358,plain,
% 1.45/1.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[186, 4357])).
% 1.45/1.60 tff(4359,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 1.45/1.60 tff(4360,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4361,plain,
% 1.45/1.60 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(4362,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[4361])).
% 1.45/1.60 tff(4363,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.60 inference(transitivity,[status(thm)],[4362, 4360])).
% 1.45/1.60 tff(4364,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(4365,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4364, 4363])).
% 1.45/1.60 tff(4366,plain,
% 1.45/1.60 ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4365, 108])).
% 1.45/1.60 tff(4367,plain,
% 1.45/1.60 (~r(elem!1, s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4366, 1059, 3244, 97])).
% 1.45/1.60 tff(4368,plain,
% 1.45/1.60 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[1677])).
% 1.45/1.60 tff(4369,plain,
% 1.45/1.60 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.60 inference(symmetry,[status(thm)],[4368])).
% 1.45/1.60 tff(4370,plain,
% 1.45/1.60 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[4369])).
% 1.45/1.60 tff(4371,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.45/1.60 tff(4372,plain,
% 1.45/1.60 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[4371, 4370])).
% 1.45/1.60 tff(4373,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[491, 4372])).
% 1.45/1.60 tff(4374,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(4375,plain,
% 1.45/1.61 (~(s(s(z)) = elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4374, 4367, 491])).
% 1.45/1.61 tff(4376,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4377,plain,
% 1.45/1.61 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4378,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(s(z)))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4377])).
% 1.45/1.61 tff(4379,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[4378, 4376])).
% 1.45/1.61 tff(4380,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4381,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(s(z)))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4380, 4379])).
% 1.45/1.61 tff(4382,plain,
% 1.45/1.61 ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4381, 108])).
% 1.45/1.61 tff(4383,plain,
% 1.45/1.61 (~r(elem!1, s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4382, 1059, 701, 97])).
% 1.45/1.61 tff(4384,plain,
% 1.45/1.61 (elem!1 = s(s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1236, 4383, 4359])).
% 1.45/1.61 tff(4385,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1697, 4384, 4375])).
% 1.45/1.61 tff(4386,plain,((~r(elem!1, z)) | b(elem!1, s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(4387,plain,
% 1.45/1.61 (~r(elem!1, z)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4386, 4359, 491, 4304, 79, 3244])).
% 1.45/1.61 tff(4388,plain,
% 1.45/1.61 (b(elem!1, z)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1037, 4387, 1046])).
% 1.45/1.61 tff(4389,plain,
% 1.45/1.61 (b(elem!1, z) <=> b(s(s(z)), z)),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1694])).
% 1.45/1.61 tff(4390,plain,
% 1.45/1.61 (b(s(s(z)), z) <=> b(elem!1, z)),
% 1.45/1.61 inference(symmetry,[status(thm)],[4389])).
% 1.45/1.61 tff(4391,plain,
% 1.45/1.61 ((~b(s(s(z)), z)) <=> (~b(elem!1, z))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4390])).
% 1.45/1.61 tff(4392,plain,
% 1.45/1.61 (~b(elem!1, z)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[368, 4391])).
% 1.45/1.61 tff(4393,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[809, 4392])).
% 1.45/1.61 tff(4394,plain,((~(elem!1 = s(s(z)))) | (~b(elem!1, z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(4395,plain,
% 1.45/1.61 (~(elem!1 = s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4394, 4388, 368])).
% 1.45/1.61 tff(4396,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4397,plain,
% 1.45/1.61 (((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4398,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4397])).
% 1.45/1.61 tff(4399,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[4398, 4396])).
% 1.45/1.61 tff(4400,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4401,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4400, 4399])).
% 1.45/1.61 tff(4402,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4401, 108, 701, 862, 2240, 97])).
% 1.45/1.61 tff(4403,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(4404,plain,
% 1.45/1.61 (~r(s(s(s(z))), elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4403, 79, 4305, 4304])).
% 1.45/1.61 tff(4405,plain,
% 1.45/1.61 (b(z, s(s(s(z))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[921, 1025])).
% 1.45/1.61 tff(4406,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[54, 4405])).
% 1.45/1.61 tff(4407,plain,((~(s(s(s(z))) = elem!1)) | b(z, s(s(s(z)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(4408,plain,
% 1.45/1.61 (~b(z, elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4407, 834, 54])).
% 1.45/1.61 tff(4409,plain,
% 1.45/1.61 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.45/1.61 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.61 tff(4410,plain,
% 1.45/1.61 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4409])).
% 1.45/1.61 tff(4411,plain,
% 1.45/1.61 (~b(s(s(z)), elem!1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4303, 4410])).
% 1.45/1.61 tff(4412,plain,
% 1.45/1.61 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(s(z))), s(s(z))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[3730])).
% 1.45/1.61 tff(4413,plain,
% 1.45/1.61 (~b(s(s(s(z))), s(s(z)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4359, 4412])).
% 1.45/1.61 tff(4414,plain,
% 1.45/1.61 (r(s(s(s(z))), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[340, 4413])).
% 1.45/1.61 tff(4415,plain,
% 1.45/1.61 (b(s(elem!1), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.61 tff(4416,plain,
% 1.45/1.61 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.45/1.61 inference(symmetry,[status(thm)],[4415])).
% 1.45/1.61 tff(4417,plain,
% 1.45/1.61 (r(s(elem!1), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.61 tff(4418,plain,
% 1.45/1.61 ((~r(s(elem!1), s(s(z)))) <=> (~r(s(s(s(s(z)))), s(s(z))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4417])).
% 1.45/1.61 tff(4419,plain,
% 1.45/1.61 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.61 tff(4420,plain,
% 1.45/1.61 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.45/1.61 inference(symmetry,[status(thm)],[4419])).
% 1.45/1.61 tff(4421,plain,
% 1.45/1.61 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.45/1.61 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.61 tff(4422,plain,
% 1.45/1.61 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[130, 4421])).
% 1.45/1.61 tff(4423,plain,
% 1.45/1.61 (r(s(elem!1), elem!1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4422, 4420])).
% 1.45/1.61 tff(4424,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.45/1.61 tff(4425,plain,
% 1.45/1.61 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.61 tff(4426,plain,
% 1.45/1.61 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.45/1.61 inference(transitivity,[status(thm)],[4425, 1004])).
% 1.45/1.61 tff(4427,plain,
% 1.45/1.61 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4426])).
% 1.45/1.61 tff(4428,plain,
% 1.45/1.61 (~(s(s(z)) = elem!1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[171, 4427])).
% 1.45/1.61 tff(4429,plain,
% 1.45/1.61 (r(s(s(z)), elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1175, 4428, 4424])).
% 1.45/1.61 tff(4430,plain,
% 1.45/1.61 (r(s(s(s(z))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.61 tff(4431,plain,
% 1.45/1.61 (r(elem!1, s(s(z)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[492, 4430])).
% 1.45/1.61 tff(4432,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4433,plain,
% 1.45/1.61 (((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4434,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4433])).
% 1.45/1.61 tff(4435,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[4434, 4432])).
% 1.45/1.61 tff(4436,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4437,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4436, 4435])).
% 1.45/1.61 tff(4438,plain,
% 1.45/1.61 (~r(s(elem!1), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4437, 108, 4431, 4429, 4423])).
% 1.45/1.61 tff(4439,plain,
% 1.45/1.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4438, 4418])).
% 1.45/1.61 tff(4440,plain,
% 1.45/1.61 (b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[462, 4439])).
% 1.45/1.61 tff(4441,plain,
% 1.45/1.61 (b(s(elem!1), s(s(z)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4440, 4416])).
% 1.45/1.61 tff(4442,plain,
% 1.45/1.61 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.61 tff(4443,plain,
% 1.45/1.61 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(elem!1))),
% 1.45/1.61 inference(symmetry,[status(thm)],[4442])).
% 1.45/1.61 tff(4444,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4445,plain,
% 1.45/1.61 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4446,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4445])).
% 1.45/1.61 tff(4447,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[4446, 4444])).
% 1.45/1.61 tff(4448,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4449,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4448, 4447])).
% 1.45/1.61 tff(4450,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4449, 108, 994, 1213, 780, 491])).
% 1.45/1.61 tff(4451,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(4452,plain,
% 1.45/1.61 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4451, 4429, 4422, 4431])).
% 1.45/1.61 tff(4453,plain,
% 1.45/1.61 (b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[440, 4452])).
% 1.45/1.61 tff(4454,plain,
% 1.45/1.61 (b(s(s(z)), s(elem!1))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4453, 4443])).
% 1.45/1.61 tff(4455,plain,
% 1.45/1.61 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.45/1.61 inference(commutativity,[status(thm)],[])).
% 1.45/1.61 tff(4456,plain,
% 1.45/1.61 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.45/1.61 inference(symmetry,[status(thm)],[4455])).
% 1.45/1.61 tff(4457,plain,
% 1.45/1.61 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4456])).
% 1.45/1.61 tff(4458,plain,
% 1.45/1.61 (~(z = s(elem!1))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1346, 4457])).
% 1.45/1.61 tff(4459,plain,
% 1.45/1.61 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.45/1.61 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.61 tff(4460,plain,
% 1.45/1.61 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.45/1.61 inference(transitivity,[status(thm)],[4459, 799])).
% 1.45/1.61 tff(4461,plain,
% 1.45/1.61 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4460])).
% 1.45/1.61 tff(4462,plain,
% 1.45/1.61 (~(z = elem!1)),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[65, 4461])).
% 1.45/1.61 tff(4463,plain,
% 1.45/1.61 (r(z, elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[934, 4462, 1027])).
% 1.45/1.61 tff(4464,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4465,plain,
% 1.45/1.61 (((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4466,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4465])).
% 1.45/1.61 tff(4467,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[4466, 4464])).
% 1.45/1.61 tff(4468,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4469,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4468, 4467])).
% 1.45/1.61 tff(4470,plain,
% 1.45/1.61 (~r(z, s(elem!1))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4469, 108, 4463, 4431, 4423])).
% 1.45/1.61 tff(4471,plain,
% 1.45/1.61 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4472,plain,
% 1.45/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4473,plain,
% 1.45/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 1.45/1.61 tff(4474,plain,
% 1.45/1.61 ((z = s(elem!1)) | b(z, s(elem!1))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4473, 45, 4470])).
% 1.45/1.61 tff(4475,plain,
% 1.45/1.61 (b(z, s(elem!1))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4474, 4458])).
% 1.45/1.61 tff(4476,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4477,plain,
% 1.45/1.61 (((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4478,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4477])).
% 1.45/1.61 tff(4479,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[4478, 4476])).
% 1.45/1.61 tff(4480,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4481,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4480, 4479])).
% 1.45/1.61 tff(4482,plain,
% 1.45/1.61 (~r(s(s(z)), z)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4481, 108, 4463, 4431, 4429])).
% 1.45/1.61 tff(4483,plain,
% 1.45/1.61 (b(s(s(z)), z)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[372, 45, 32, 4482])).
% 1.45/1.61 tff(4484,plain,
% 1.45/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4485,plain,
% 1.45/1.61 (((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(4486,plain,
% 1.45/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[4485])).
% 1.45/1.61 tff(4487,plain,
% 1.45/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[4486, 4484])).
% 1.45/1.61 tff(4488,plain,
% 1.45/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(4489,plain,
% 1.45/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[4488, 4487])).
% 1.45/1.61 tff(4490,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4489, 233, 4483, 4475, 4454, 4441])).
% 1.45/1.62 tff(4491,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(z)), elem!1) | b(z, elem!1) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4492,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4491, 4414, 4411, 4408, 834, 130])).
% 1.45/1.62 tff(4493,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(s(s(z)), s(s(s(z)))) | b(elem!1, s(s(z))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4494,plain,
% 1.45/1.62 (~(s(s(s(z))) = elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4493, 4359, 4303, 130, 54])).
% 1.45/1.62 tff(4495,plain,
% 1.45/1.62 (b(s(s(s(z))), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[843, 4494, 4404])).
% 1.45/1.62 tff(4496,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4497,plain,
% 1.45/1.62 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4498,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4497])).
% 1.45/1.62 tff(4499,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4498, 4496])).
% 1.45/1.62 tff(4500,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(4501,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4500, 4499])).
% 1.45/1.62 tff(4502,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4501, 233, 809, 707, 920, 284])).
% 1.45/1.62 tff(4503,plain,((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4504,plain,
% 1.45/1.62 (~b(s(s(z)), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4503, 4388, 284, 4495])).
% 1.45/1.62 tff(4505,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 1.45/1.62 tff(4506,plain,
% 1.45/1.62 (r(elem!1, s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1236, 4505, 4359])).
% 1.45/1.62 tff(4507,plain,
% 1.45/1.62 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4451, 1213, 780, 994])).
% 1.45/1.62 tff(4508,plain,
% 1.45/1.62 (b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[440, 4507])).
% 1.45/1.62 tff(4509,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4510,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(4511,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4510, 4509])).
% 1.45/1.62 tff(4512,plain,
% 1.45/1.62 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4511, 108, 994, 1213, 780])).
% 1.45/1.62 tff(4513,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[462, 4512])).
% 1.45/1.62 tff(4514,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[3431, 233, 284, 4513, 4508, 204])).
% 1.45/1.62 tff(4515,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4516,plain,
% 1.45/1.62 (~r(s(s(z)), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4515, 4506, 204, 284, 780])).
% 1.45/1.62 tff(4517,plain,
% 1.45/1.62 (s(s(z)) = elem!1),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1175, 4516, 4424])).
% 1.45/1.62 tff(4518,plain,
% 1.45/1.62 (elem!1 = s(s(z))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4517, 791])).
% 1.45/1.62 tff(4519,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4505, 4518])).
% 1.45/1.62 tff(4520,plain,((elem!1 = s(s(z))) | b(s(s(z)), elem!1) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | b(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4521,plain,
% 1.45/1.62 (~r(s(s(s(s(z)))), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4520, 4504, 4358, 284, 4395, 4359])).
% 1.45/1.62 tff(4522,plain,
% 1.45/1.62 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[3354, 79, 3244, 4304])).
% 1.45/1.62 tff(4523,plain,
% 1.45/1.62 (r(elem!1, s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1236, 4395, 4359])).
% 1.45/1.62 tff(4524,plain,
% 1.45/1.62 (~(s(s(s(s(z)))) = elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[997, 4523, 4522])).
% 1.45/1.62 tff(4525,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[860, 4524, 4521])).
% 1.45/1.62 tff(4526,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4527,plain,
% 1.45/1.62 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4528,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4527])).
% 1.45/1.62 tff(4529,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4528, 4526])).
% 1.45/1.62 tff(4530,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(4531,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4530, 4529])).
% 1.45/1.62 tff(4532,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4531, 233, 4388, 4495, 4525, 4358])).
% 1.45/1.62 tff(4533,plain,(b(elem!1, s(s(z))) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(z)), z) | (elem!1 = z) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4534,plain,
% 1.45/1.62 (b(z, s(s(s(z))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4533, 4356, 368, 1632, 491, 3244, 4303, 130, 284])).
% 1.45/1.62 tff(4535,plain,
% 1.45/1.62 (~b(elem!1, z)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4503, 920, 284, 707])).
% 1.45/1.62 tff(4536,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4537,plain,
% 1.45/1.62 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4538,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4537])).
% 1.45/1.62 tff(4539,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4538, 4536])).
% 1.45/1.62 tff(4540,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(4541,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4540, 4539])).
% 1.45/1.62 tff(4542,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4541, 233, 920, 284, 273, 706])).
% 1.45/1.62 tff(4543,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4544,plain,
% 1.45/1.62 (~b(z, s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4543, 920, 284, 273])).
% 1.45/1.62 tff(4545,plain,
% 1.45/1.62 (r(z, s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[357, 45, 353, 352])).
% 1.45/1.62 tff(4546,plain,
% 1.45/1.62 (b(z, elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[934, 717, 2848])).
% 1.45/1.62 tff(4547,plain,
% 1.45/1.62 (b(z, elem!1) <=> b(z, s(s(z)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1694])).
% 1.45/1.62 tff(4548,plain,
% 1.45/1.62 (b(z, s(s(z))) <=> b(z, elem!1)),
% 1.45/1.62 inference(symmetry,[status(thm)],[4547])).
% 1.45/1.62 tff(4549,plain,
% 1.45/1.62 ((~b(z, s(s(z)))) <=> (~b(z, elem!1))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4548])).
% 1.45/1.62 tff(4550,plain,
% 1.45/1.62 (~b(z, elem!1)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[353, 4549])).
% 1.45/1.62 tff(4551,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[921, 4550])).
% 1.45/1.62 tff(4552,plain,((~(elem!1 = s(s(z)))) | (~b(z, elem!1)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4553,plain,
% 1.45/1.62 (~(elem!1 = s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4552, 4546, 353])).
% 1.45/1.62 tff(4554,plain,
% 1.45/1.62 (r(elem!1, s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1236, 4553, 4359])).
% 1.45/1.62 tff(4555,plain,
% 1.45/1.62 (r(elem!1, z)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1037, 1632, 1033])).
% 1.45/1.62 tff(4556,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4557,plain,
% 1.45/1.62 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4558,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4557])).
% 1.45/1.62 tff(4559,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4558, 4556])).
% 1.45/1.62 tff(4560,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, z)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(4561,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(s(z))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4560, 4559])).
% 1.45/1.62 tff(4562,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4561, 108, 4555, 4554, 701, 4545])).
% 1.45/1.62 tff(4563,plain,((z = elem!1) | (~r(s(s(z)), z)) | b(z, s(s(z))) | b(elem!1, s(s(z))) | b(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4564,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4563, 4544, 4535, 701, 2848, 4359, 717])).
% 1.45/1.62 tff(4565,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | r(z, elem!1) | b(elem!1, s(s(z))) | (z = elem!1) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4566,plain,
% 1.45/1.62 (~b(s(s(z)), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4565, 2848, 4304, 4356, 717, 284, 4534, 707])).
% 1.45/1.62 tff(4567,plain,
% 1.45/1.62 (s(s(z)) = elem!1),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1175, 4566, 1811])).
% 1.45/1.62 tff(4568,plain,
% 1.45/1.62 (s(s(s(z))) = s(elem!1)),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1677])).
% 1.45/1.62 tff(4569,plain,
% 1.45/1.62 (s(elem!1) = s(s(s(z)))),
% 1.45/1.62 inference(symmetry,[status(thm)],[4568])).
% 1.45/1.62 tff(4570,plain,
% 1.45/1.62 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4569])).
% 1.45/1.62 tff(4571,plain,
% 1.45/1.62 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.45/1.62 inference(symmetry,[status(thm)],[4570])).
% 1.45/1.62 tff(4572,plain,
% 1.45/1.62 (b(s(elem!1), s(z))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1072, 4571])).
% 1.45/1.62 tff(4573,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1320, 4572])).
% 1.45/1.62 tff(4574,plain,(b(s(elem!1), s(z)) | (~b(s(s(s(z))), s(z))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4575,plain,
% 1.45/1.62 (b(s(elem!1), s(z))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4574, 4567, 4344])).
% 1.45/1.62 tff(4576,plain,
% 1.45/1.62 (elem!1 = s(s(z))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1677, 791])).
% 1.45/1.62 tff(4577,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4505, 4576])).
% 1.45/1.62 tff(4578,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4579,plain,
% 1.45/1.62 (elem!1 = s(s(z))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4578, 4567])).
% 1.45/1.62 tff(4580,plain,
% 1.45/1.62 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4567])).
% 1.45/1.62 tff(4581,plain,
% 1.45/1.62 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.45/1.62 inference(transitivity,[status(thm)],[4580, 808])).
% 1.45/1.62 tff(4582,plain,
% 1.45/1.62 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4581])).
% 1.45/1.62 tff(4583,plain,
% 1.45/1.62 (~(s(s(s(s(z)))) = elem!1)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[169, 4582])).
% 1.45/1.62 tff(4584,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[860, 999, 1070])).
% 1.45/1.62 tff(4585,plain,
% 1.45/1.62 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1694])).
% 1.45/1.62 tff(4586,plain,
% 1.45/1.62 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1694])).
% 1.45/1.62 tff(4587,plain,
% 1.45/1.62 ((s(s(s(s(z)))) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4586, 143])).
% 1.45/1.62 tff(4588,plain,
% 1.45/1.62 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.45/1.62 inference(symmetry,[status(thm)],[4587])).
% 1.45/1.62 tff(4589,plain,
% 1.45/1.62 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4588, 852])).
% 1.45/1.62 tff(4590,plain,
% 1.45/1.62 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4589])).
% 1.45/1.62 tff(4591,plain,
% 1.45/1.62 (~(elem!1 = s(s(s(s(z)))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[169, 4590])).
% 1.45/1.62 tff(4592,plain,
% 1.45/1.62 (b(elem!1, s(s(s(s(z)))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[850, 846, 4371])).
% 1.45/1.62 tff(4593,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[860, 856, 999])).
% 1.45/1.62 tff(4594,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4595,plain,
% 1.45/1.62 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4596,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4595])).
% 1.45/1.62 tff(4597,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4596, 4594])).
% 1.45/1.62 tff(4598,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(4599,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4598, 4597])).
% 1.45/1.62 tff(4600,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4599, 233, 707, 4593, 4592, 204])).
% 1.45/1.62 tff(4601,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4602,plain,
% 1.45/1.62 (r(elem!1, s(s(s(s(z)))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4601, 4591, 999, 707, 204])).
% 1.45/1.62 tff(4603,plain,
% 1.45/1.62 (r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4602, 4585])).
% 1.45/1.62 tff(4604,plain,
% 1.45/1.62 (~r(s(s(z)), s(z))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1876, 108, 130, 4603, 52])).
% 1.45/1.62 tff(4605,plain,
% 1.45/1.62 (b(s(s(z)), s(z))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[48, 45, 35, 4604])).
% 1.45/1.62 tff(4606,plain,
% 1.45/1.62 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[1694])).
% 1.45/1.62 tff(4607,plain,
% 1.45/1.62 (s(s(z)) = elem!1),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1697, 1694])).
% 1.45/1.62 tff(4608,plain,
% 1.45/1.62 (~(s(z) = elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1687, 4607])).
% 1.45/1.62 tff(4609,plain,
% 1.45/1.62 (s(s(z)) = elem!1),
% 1.45/1.62 inference(symmetry,[status(thm)],[1694])).
% 1.45/1.62 tff(4610,plain,
% 1.45/1.62 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4609])).
% 1.45/1.62 tff(4611,plain,
% 1.45/1.62 ((~r(s(z), s(s(z)))) <=> (~r(s(z), elem!1))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4610])).
% 1.45/1.62 tff(4612,plain,
% 1.45/1.62 (~r(s(z), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1884, 108, 130, 4603, 52])).
% 1.45/1.62 tff(4613,plain,
% 1.45/1.62 (~r(s(z), elem!1)),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4612, 4611])).
% 1.45/1.62 tff(4614,plain,
% 1.45/1.62 (b(s(z), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1130, 4613, 4608])).
% 1.45/1.62 tff(4615,plain,
% 1.45/1.62 (b(s(z), s(s(z)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4614, 4606])).
% 1.45/1.62 tff(4616,plain,
% 1.45/1.62 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(4617,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[4616])).
% 1.45/1.62 tff(4618,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[4617, 1887])).
% 1.45/1.62 tff(4619,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(4620,plain,
% 1.45/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[4619, 4618])).
% 1.45/1.62 tff(4621,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4620, 233, 284, 4615, 1072, 4605])).
% 1.45/1.62 tff(4622,plain,((~(elem!1 = s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(4623,plain,
% 1.45/1.62 (~r(s(z), s(s(s(s(z)))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4622, 999, 284, 130, 1072, 1694, 707, 204])).
% 1.45/1.62 tff(4624,plain,
% 1.45/1.62 (b(s(z), s(s(s(s(z)))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1122, 4623])).
% 1.45/1.62 tff(4625,plain,
% 1.45/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4626,plain,
% 1.45/1.63 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4627,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4626])).
% 1.45/1.63 tff(4628,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[4627, 4625])).
% 1.45/1.63 tff(4629,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4630,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4629, 4628])).
% 1.45/1.63 tff(4631,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4630, 233, 1071, 204, 1072, 2854])).
% 1.45/1.63 tff(4632,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(4633,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4632, 4624, 4584, 204, 1072])).
% 1.45/1.63 tff(4634,plain,(r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~(elem!1 = s(s(z)))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(4635,plain,
% 1.45/1.63 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4634, 4583, 4344, 4358, 284, 130, 4579, 707])).
% 1.45/1.63 tff(4636,plain,
% 1.45/1.63 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4568])).
% 1.45/1.63 tff(4637,plain,
% 1.45/1.63 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.45/1.63 inference(symmetry,[status(thm)],[4636])).
% 1.45/1.63 tff(4638,plain,
% 1.45/1.63 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4637])).
% 1.45/1.63 tff(4639,plain,
% 1.45/1.63 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.45/1.63 inference(symmetry,[status(thm)],[4638])).
% 1.45/1.63 tff(4640,plain,
% 1.45/1.63 (r(s(s(elem!1)), elem!1)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[780, 4639])).
% 1.45/1.63 tff(4641,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1539, 4640])).
% 1.45/1.63 tff(4642,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(elem!1)), elem!1) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(4643,plain,
% 1.45/1.63 (r(s(s(elem!1)), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4642, 4635, 4567])).
% 1.45/1.63 tff(4644,plain,
% 1.45/1.63 (s(s(s(z))) = s(elem!1)),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4567])).
% 1.45/1.63 tff(4645,plain,
% 1.45/1.63 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4644])).
% 1.45/1.63 tff(4646,plain,
% 1.45/1.63 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.45/1.63 inference(symmetry,[status(thm)],[4645])).
% 1.45/1.63 tff(4647,plain,
% 1.45/1.63 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4646])).
% 1.45/1.63 tff(4648,plain,
% 1.45/1.63 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 1.45/1.63 inference(symmetry,[status(thm)],[4647])).
% 1.45/1.63 tff(4649,plain,
% 1.45/1.63 (r(elem!1, s(s(s(s(z)))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4374, 4567, 491])).
% 1.45/1.63 tff(4650,plain,
% 1.45/1.63 (r(elem!1, s(s(elem!1)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4649, 4648])).
% 1.45/1.63 tff(4651,plain,
% 1.45/1.63 (~(s(z) = elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1687, 4567])).
% 1.45/1.63 tff(4652,plain,
% 1.45/1.63 (s(elem!1) = s(s(s(z)))),
% 1.45/1.63 inference(symmetry,[status(thm)],[4644])).
% 1.45/1.63 tff(4653,plain,
% 1.45/1.63 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4652])).
% 1.45/1.63 tff(4654,plain,
% 1.45/1.63 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.45/1.63 inference(symmetry,[status(thm)],[4653])).
% 1.45/1.63 tff(4655,plain,
% 1.45/1.63 (b(s(elem!1), elem!1)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[707, 4654])).
% 1.45/1.63 tff(4656,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.45/1.63 tff(4657,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4658,plain,
% 1.45/1.63 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4659,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4658])).
% 1.45/1.63 tff(4660,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[4659, 4657])).
% 1.45/1.63 tff(4661,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4662,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4661, 4660])).
% 1.45/1.63 tff(4663,plain,
% 1.45/1.63 (~r(elem!1, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4662, 108, 1388, 1387, 4656])).
% 1.45/1.63 tff(4664,plain,
% 1.45/1.63 (b(elem!1, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[965, 4663, 1654])).
% 1.45/1.63 tff(4665,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4666,plain,
% 1.45/1.63 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4667,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4666])).
% 1.45/1.63 tff(4668,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[4667, 4665])).
% 1.45/1.63 tff(4669,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4670,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4669, 4668])).
% 1.45/1.63 tff(4671,plain,
% 1.45/1.63 (~r(s(z), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4670, 108, 1388, 1387, 4656])).
% 1.45/1.63 tff(4672,plain,
% 1.45/1.63 (b(s(z), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1130, 4671, 954])).
% 1.45/1.63 tff(4673,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4674,plain,
% 1.45/1.63 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4675,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4674])).
% 1.45/1.63 tff(4676,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[4675, 4673])).
% 1.45/1.63 tff(4677,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4678,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4677, 4676])).
% 1.45/1.63 tff(4679,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4678, 233, 4672, 1289, 4664, 1327])).
% 1.45/1.63 tff(4680,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (s(z) = elem!1) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(4681,plain,
% 1.45/1.63 (~r(s(z), s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4680, 4655, 4575, 4651, 4650, 4643])).
% 1.45/1.63 tff(4682,plain,
% 1.45/1.63 (b(s(z), s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1352, 4681])).
% 1.45/1.63 tff(4683,plain,
% 1.45/1.63 (~(elem!1 = s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[956, 4651])).
% 1.45/1.63 tff(4684,plain,
% 1.45/1.63 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.45/1.63 inference(commutativity,[status(thm)],[])).
% 1.45/1.63 tff(4685,plain,
% 1.45/1.63 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.45/1.63 inference(symmetry,[status(thm)],[4684])).
% 1.45/1.63 tff(4686,plain,
% 1.45/1.63 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4685])).
% 1.45/1.63 tff(4687,plain,
% 1.45/1.63 (~(s(s(elem!1)) = s(z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[1348, 4686])).
% 1.45/1.63 tff(4688,plain,
% 1.45/1.63 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4644, 4645])).
% 1.45/1.63 tff(4689,plain,
% 1.45/1.63 (b(s(elem!1), s(s(elem!1)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4358, 4688])).
% 1.45/1.63 tff(4690,plain,
% 1.45/1.63 (~b(s(s(elem!1)), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1336, 4682, 4689, 4575])).
% 1.45/1.63 tff(4691,plain,
% 1.45/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4692,plain,
% 1.45/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4693,plain,
% 1.45/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4692, 4691])).
% 1.45/1.63 tff(4694,plain,
% 1.45/1.63 ((s(s(elem!1)) = s(z)) | r(s(s(elem!1)), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4693, 45, 4690])).
% 1.45/1.63 tff(4695,plain,
% 1.45/1.63 (r(s(s(elem!1)), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4694, 4687])).
% 1.45/1.63 tff(4696,plain,
% 1.45/1.63 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4644])).
% 1.45/1.63 tff(4697,plain,
% 1.45/1.63 (b(s(elem!1), z)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4346, 4696])).
% 1.45/1.63 tff(4698,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4699,plain,
% 1.45/1.63 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4700,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4699])).
% 1.45/1.63 tff(4701,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[4700, 4698])).
% 1.45/1.63 tff(4702,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4703,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4702, 4701])).
% 1.45/1.63 tff(4704,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4703, 233, 921, 402, 1459, 1327])).
% 1.45/1.63 tff(4705,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(4706,plain,
% 1.45/1.63 (~b(s(z), z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4705, 4347, 4697, 4575])).
% 1.45/1.63 tff(4707,plain,
% 1.45/1.63 (r(s(z), z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[260, 4706])).
% 1.45/1.63 tff(4708,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4709,plain,
% 1.45/1.63 (((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4710,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4709])).
% 1.45/1.63 tff(4711,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[4710, 4708])).
% 1.45/1.63 tff(4712,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4713,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4712, 4711])).
% 1.45/1.63 tff(4714,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4713, 108, 1389, 246, 1387, 1525])).
% 1.45/1.63 tff(4715,plain,((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(4716,plain,
% 1.45/1.63 (~r(elem!1, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4715, 4707, 4650, 4695])).
% 1.45/1.63 tff(4717,plain,
% 1.45/1.63 (b(elem!1, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[965, 4716, 4683])).
% 1.45/1.63 tff(4718,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4719,plain,
% 1.45/1.63 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(4720,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[4719])).
% 1.45/1.63 tff(4721,plain,
% 1.45/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[4720, 4718])).
% 1.45/1.63 tff(4722,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(4723,plain,
% 1.45/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[4722, 4721])).
% 1.45/1.63 tff(4724,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4723, 233, 4655, 4717, 4682, 4575])).
% 1.45/1.63 tff(4725,plain,(r(z, elem!1) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | r(s(s(z)), elem!1) | (z = elem!1) | b(s(s(z)), z) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4726,plain,
% 1.45/1.64 (r(z, elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4725, 4342, 130, 284, 491, 1811, 717, 368, 3244, 4303])).
% 1.45/1.64 tff(4727,plain,
% 1.45/1.64 (~(elem!1 = s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1697, 1212])).
% 1.45/1.64 tff(4728,plain,
% 1.45/1.64 (b(s(s(z)), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1175, 1212, 1811])).
% 1.45/1.64 tff(4729,plain,
% 1.45/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4730,plain,
% 1.45/1.64 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4731,plain,
% 1.45/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4730])).
% 1.45/1.64 tff(4732,plain,
% 1.45/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4731, 4729])).
% 1.45/1.64 tff(4733,plain,
% 1.45/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(4734,plain,
% 1.45/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4733, 4732])).
% 1.45/1.64 tff(4735,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4734, 233, 1009, 707, 920, 284])).
% 1.45/1.64 tff(4736,plain,((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4737,plain,
% 1.45/1.64 (~b(elem!1, s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4736, 4728, 707, 284])).
% 1.45/1.64 tff(4738,plain,
% 1.45/1.64 (r(elem!1, s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1236, 4737, 4727])).
% 1.45/1.64 tff(4739,plain,
% 1.45/1.64 (~b(elem!1, z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4503, 4728, 284, 707])).
% 1.45/1.64 tff(4740,plain,
% 1.45/1.64 (r(elem!1, z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1037, 4739, 1046])).
% 1.45/1.64 tff(4741,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4742,plain,
% 1.45/1.64 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4743,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4742])).
% 1.45/1.64 tff(4744,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4743, 4741])).
% 1.45/1.64 tff(4745,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(4746,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4745, 4744])).
% 1.45/1.64 tff(4747,plain,
% 1.45/1.64 ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4746, 108])).
% 1.45/1.64 tff(4748,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4747, 4740, 4738, 701, 938])).
% 1.45/1.64 tff(4749,plain,((s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~r(z, elem!1)) | (elem!1 = z) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4750,plain,
% 1.45/1.64 (s(s(z)) = elem!1),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4749, 4726, 4304, 1632, 284, 4342, 1811])).
% 1.45/1.64 tff(4751,plain,
% 1.45/1.64 (b(s(s(z)), elem!1) <=> b(elem!1, elem!1)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4750])).
% 1.45/1.64 tff(4752,plain,
% 1.45/1.64 (b(elem!1, elem!1) <=> b(s(s(z)), elem!1)),
% 1.45/1.64 inference(symmetry,[status(thm)],[4751])).
% 1.45/1.64 tff(4753,plain,
% 1.45/1.64 ((~b(elem!1, elem!1)) <=> (~b(s(s(z)), elem!1))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4752])).
% 1.45/1.64 tff(4754,plain,
% 1.45/1.64 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.45/1.64 inference(bind,[status(th)],[])).
% 1.45/1.64 tff(4755,plain,
% 1.45/1.64 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.45/1.64 inference(quant_intro,[status(thm)],[4754])).
% 1.45/1.64 tff(4756,plain,
% 1.45/1.64 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4757,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 1.45/1.64 tff(4758,plain,
% 1.45/1.64 (![X: $i] : (~b(X, X))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4757, 4756])).
% 1.45/1.64 tff(4759,plain,(
% 1.45/1.64 ![X: $i] : (~b(X, X))),
% 1.45/1.64 inference(skolemize,[status(sab)],[4758])).
% 1.45/1.64 tff(4760,plain,
% 1.45/1.64 (![X: $i] : (~b(X, X))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4759, 4755])).
% 1.45/1.64 tff(4761,plain,
% 1.45/1.64 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(4762,plain,
% 1.45/1.64 (~b(elem!1, elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4761, 4760])).
% 1.45/1.64 tff(4763,plain,
% 1.45/1.64 (~b(s(s(z)), elem!1)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4762, 4753])).
% 1.45/1.64 tff(4764,plain,
% 1.45/1.64 (~(elem!1 = s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1051, 1049])).
% 1.45/1.64 tff(4765,plain,
% 1.45/1.64 (b(s(s(z)), s(s(s(z))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[919, 3721])).
% 1.45/1.64 tff(4766,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4303, 4765])).
% 1.45/1.64 tff(4767,plain,((~(s(s(z)) = elem!1)) | b(s(s(z)), s(s(s(z)))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4768,plain,
% 1.45/1.64 (~b(elem!1, s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4767, 4750, 4303])).
% 1.45/1.64 tff(4769,plain,
% 1.45/1.64 (r(elem!1, s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[886, 4768, 4764])).
% 1.45/1.64 tff(4770,plain,
% 1.45/1.64 (r(z, s(s(z))) <=> r(z, elem!1)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4750])).
% 1.45/1.64 tff(4771,plain,
% 1.45/1.64 (r(z, elem!1) <=> r(z, s(s(z)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[4770])).
% 1.45/1.64 tff(4772,plain,
% 1.45/1.64 (r(z, s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4726, 4771])).
% 1.45/1.64 tff(4773,plain,
% 1.45/1.64 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3276, 4772, 3244, 4305])).
% 1.45/1.64 tff(4774,plain,
% 1.45/1.64 (elem!1 = s(s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4578, 4750])).
% 1.45/1.64 tff(4775,plain,
% 1.45/1.64 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4750])).
% 1.45/1.64 tff(4776,plain,
% 1.45/1.64 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.45/1.64 inference(transitivity,[status(thm)],[4775, 808])).
% 1.45/1.64 tff(4777,plain,
% 1.45/1.64 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4776])).
% 1.45/1.64 tff(4778,plain,
% 1.45/1.64 (~(s(s(s(s(z)))) = elem!1)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[169, 4777])).
% 1.45/1.64 tff(4779,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4634, 4778, 4344, 4358, 284, 130, 4774, 4342])).
% 1.45/1.64 tff(4780,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4781,plain,
% 1.45/1.64 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4782,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4781])).
% 1.45/1.64 tff(4783,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4782, 4780])).
% 1.45/1.64 tff(4784,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(4785,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4784, 4783])).
% 1.45/1.64 tff(4786,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4785, 108, 1213, 780, 888, 491])).
% 1.45/1.64 tff(4787,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4788,plain,
% 1.45/1.64 (~r(s(s(z)), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4787, 780, 888, 491])).
% 1.45/1.64 tff(4789,plain,
% 1.45/1.64 (s(s(z)) = elem!1),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1175, 4788, 4424])).
% 1.45/1.64 tff(4790,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4789])).
% 1.45/1.64 tff(4791,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[4790])).
% 1.45/1.64 tff(4792,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[780, 4791])).
% 1.45/1.64 tff(4793,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[457, 4792])).
% 1.45/1.64 tff(4794,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), s(s(z))) | b(s(s(z)), elem!1) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4795,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4794, 4779, 4773, 4769, 491, 4763])).
% 1.45/1.64 tff(4796,plain,((s(s(s(z))) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), elem!1) | (z = elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4797,plain,
% 1.45/1.64 (s(s(s(z))) = elem!1),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4796, 1811, 284, 130, 3244, 4303, 491, 717, 368])).
% 1.45/1.64 tff(4798,plain,
% 1.45/1.64 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4797])).
% 1.45/1.64 tff(4799,plain,
% 1.45/1.64 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 1.45/1.64 inference(symmetry,[status(thm)],[4798])).
% 1.45/1.64 tff(4800,plain,
% 1.45/1.64 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), s(s(s(z)))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4799])).
% 1.45/1.64 tff(4801,plain,
% 1.45/1.64 (~r(s(s(z)), s(s(s(z))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[1811, 4800])).
% 1.45/1.64 tff(4802,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4305, 4801])).
% 1.45/1.64 tff(4803,plain,(r(s(s(z)), elem!1) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (z = elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4804,plain,
% 1.45/1.64 (r(s(s(z)), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4803, 4307, 284, 3244, 4303, 491, 717, 368])).
% 1.45/1.64 tff(4805,plain,
% 1.45/1.64 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2598, 4307, 4305, 491])).
% 1.45/1.64 tff(4806,plain,
% 1.45/1.64 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[186, 4805])).
% 1.45/1.64 tff(4807,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4632, 2854, 204, 1072])).
% 1.45/1.64 tff(4808,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3241, 2854, 1072, 204])).
% 1.45/1.64 tff(4809,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[629, 45, 89, 4808])).
% 1.45/1.64 tff(4810,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[629, 45, 89, 3411])).
% 1.45/1.64 tff(4811,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.64 tff(4812,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.64 inference(symmetry,[status(thm)],[4811])).
% 1.45/1.64 tff(4813,plain,
% 1.45/1.64 (s(s(s(z))) = s(s(s(s(z))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[1265, 874])).
% 1.45/1.64 tff(4814,plain,
% 1.45/1.64 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4813])).
% 1.45/1.64 tff(4815,plain,
% 1.45/1.64 (s(s(z)) = s(s(s(s(z))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[165, 4814, 61, 1265, 874])).
% 1.45/1.64 tff(4816,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[169, 4815])).
% 1.45/1.64 tff(4817,plain,((~(elem!1 = s(s(s(z))))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4818,plain,
% 1.45/1.64 (~(elem!1 = s(s(s(s(z)))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4817, 1262])).
% 1.45/1.64 tff(4819,plain,
% 1.45/1.64 (~(s(s(s(s(z)))) = elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[855, 4818])).
% 1.45/1.64 tff(4820,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[860, 4819, 999])).
% 1.45/1.64 tff(4821,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4820, 4812])).
% 1.45/1.64 tff(4822,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4306, 4821])).
% 1.45/1.64 tff(4823,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4824,plain,
% 1.45/1.64 (~(s(s(s(z))) = elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4823, 4306, 999])).
% 1.45/1.64 tff(4825,plain,
% 1.45/1.64 (r(s(s(s(z))), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[843, 4824, 797])).
% 1.45/1.64 tff(4826,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4827,plain,
% 1.45/1.64 (((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4828,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4827])).
% 1.45/1.64 tff(4829,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4828, 4826])).
% 1.45/1.64 tff(4830,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(4831,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4830, 4829])).
% 1.45/1.64 tff(4832,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4831, 108, 4307, 4825, 97, 3244])).
% 1.45/1.64 tff(4833,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(z))), elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4834,plain,
% 1.45/1.64 (b(s(s(s(z))), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4833, 999, 4306, 97, 3244])).
% 1.45/1.64 tff(4835,plain,
% 1.45/1.64 (s(s(s(s(z)))) = elem!1),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[860, 999, 828])).
% 1.45/1.64 tff(4836,plain,
% 1.45/1.64 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4835])).
% 1.45/1.64 tff(4837,plain,
% 1.45/1.64 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4836, 791])).
% 1.45/1.64 tff(4838,plain,
% 1.45/1.64 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4837])).
% 1.45/1.64 tff(4839,plain,
% 1.45/1.64 (~(elem!1 = s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[169, 4838])).
% 1.45/1.64 tff(4840,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4835])).
% 1.45/1.64 tff(4841,plain,
% 1.45/1.64 (r(elem!1, z)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[3244, 4840])).
% 1.45/1.64 tff(4842,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4835])).
% 1.45/1.64 tff(4843,plain,
% 1.45/1.64 (r(elem!1, s(s(s(z))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4307, 4842])).
% 1.45/1.64 tff(4844,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4845,plain,
% 1.45/1.64 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4846,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z)))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4845])).
% 1.45/1.64 tff(4847,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4846, 4844])).
% 1.45/1.64 tff(4848,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(4849,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z)))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4848, 4847])).
% 1.45/1.64 tff(4850,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4849, 108, 1059, 492, 888, 97])).
% 1.45/1.64 tff(4851,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(4852,plain,
% 1.45/1.64 (~r(s(s(s(z))), s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4851, 4841, 4843, 97])).
% 1.45/1.64 tff(4853,plain,
% 1.45/1.64 (b(s(s(s(z))), s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[340, 4852])).
% 1.45/1.64 tff(4854,plain,
% 1.45/1.64 (~b(s(s(z)), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3254, 4853, 706, 272])).
% 1.45/1.64 tff(4855,plain,
% 1.45/1.64 (r(s(s(z)), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[374, 4854])).
% 1.45/1.64 tff(4856,plain,
% 1.45/1.64 (~r(elem!1, s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4382, 4855, 97, 4841])).
% 1.45/1.64 tff(4857,plain,
% 1.45/1.64 (b(elem!1, s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1236, 4856, 4839])).
% 1.45/1.64 tff(4858,plain,
% 1.45/1.64 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4835])).
% 1.45/1.64 tff(4859,plain,
% 1.45/1.64 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 1.45/1.64 inference(transitivity,[status(thm)],[4858, 799])).
% 1.45/1.64 tff(4860,plain,
% 1.45/1.64 ((~(s(s(s(s(z)))) = z)) <=> (~(z = elem!1))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4859])).
% 1.45/1.64 tff(4861,plain,
% 1.45/1.64 (~(z = elem!1)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[89, 4860])).
% 1.45/1.64 tff(4862,plain,
% 1.45/1.64 (elem!1 = s(s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[855, 4835])).
% 1.45/1.64 tff(4863,plain,
% 1.45/1.64 (~b(s(s(z)), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4736, 4857, 4834, 4853])).
% 1.45/1.64 tff(4864,plain,
% 1.45/1.64 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[874])).
% 1.45/1.64 tff(4865,plain,
% 1.45/1.64 (r(z, s(s(s(s(z)))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[938, 4864])).
% 1.45/1.64 tff(4866,plain,
% 1.45/1.64 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[874])).
% 1.45/1.64 tff(4867,plain,
% 1.45/1.64 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4866])).
% 1.45/1.64 tff(4868,plain,
% 1.45/1.64 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4424, 4867])).
% 1.45/1.64 tff(4869,plain,
% 1.45/1.64 (r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[440, 4868])).
% 1.45/1.64 tff(4870,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4871,plain,
% 1.45/1.64 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(4872,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4871])).
% 1.45/1.64 tff(4873,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4872, 4870])).
% 1.45/1.64 tff(4874,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(4875,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4874, 4873])).
% 1.45/1.64 tff(4876,plain,
% 1.45/1.64 (~r(s(s(z)), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4875, 108, 130, 4869, 4865])).
% 1.45/1.64 tff(4877,plain,
% 1.45/1.64 (b(s(s(z)), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[372, 45, 32, 4876])).
% 1.45/1.64 tff(4878,plain,
% 1.45/1.64 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.45/1.64 inference(commutativity,[status(thm)],[])).
% 1.45/1.64 tff(4879,plain,
% 1.45/1.64 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[4878])).
% 1.45/1.64 tff(4880,plain,
% 1.45/1.64 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[4879])).
% 1.45/1.64 tff(4881,plain,
% 1.45/1.64 (~(z = s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[32, 4880])).
% 1.45/1.64 tff(4882,plain,
% 1.45/1.64 ((elem!1 = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[874])).
% 1.45/1.64 tff(4883,plain,
% 1.45/1.64 ((elem!1 = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[4882, 143])).
% 1.45/1.64 tff(4884,plain,
% 1.45/1.64 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 1.45/1.65 inference(symmetry,[status(thm)],[4883])).
% 1.45/1.65 tff(4885,plain,
% 1.45/1.65 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 1.45/1.65 inference(transitivity,[status(thm)],[4884, 1004])).
% 1.45/1.65 tff(4886,plain,
% 1.45/1.65 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4885])).
% 1.45/1.65 tff(4887,plain,
% 1.45/1.65 (~(s(s(z)) = elem!1)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[169, 4886])).
% 1.45/1.65 tff(4888,plain,
% 1.45/1.65 (r(s(s(z)), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1175, 4887, 4424])).
% 1.45/1.65 tff(4889,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4890,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(4891,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4890, 4889])).
% 1.45/1.65 tff(4892,plain,
% 1.45/1.65 ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4891, 108])).
% 1.45/1.65 tff(4893,plain,
% 1.45/1.65 (~r(z, s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4892, 4888, 1059, 938])).
% 1.45/1.65 tff(4894,plain,
% 1.45/1.65 ((z = s(s(z))) | b(z, s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[357, 45, 4893])).
% 1.45/1.65 tff(4895,plain,
% 1.45/1.65 (b(z, s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4894, 4881])).
% 1.45/1.65 tff(4896,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3252, 233, 284, 4895, 4877, 272])).
% 1.45/1.65 tff(4897,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, z)) | (~r(z, elem!1)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(4898,plain,
% 1.45/1.65 (~r(z, elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4897, 4863, 272, 4862, 4307, 4841, 4853])).
% 1.45/1.65 tff(4899,plain,
% 1.45/1.65 (b(z, elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[934, 4898, 4861])).
% 1.45/1.65 tff(4900,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4353, 233, 4899, 4857, 4834, 272])).
% 1.45/1.65 tff(4901,plain,(r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(4902,plain,
% 1.45/1.65 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4901, 706, 97, 272, 4810, 4306, 828])).
% 1.45/1.65 tff(4903,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4904,plain,
% 1.45/1.65 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4905,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4904])).
% 1.45/1.65 tff(4906,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[4905, 4903])).
% 1.45/1.65 tff(4907,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(4908,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4907, 4906])).
% 1.45/1.65 tff(4909,plain,
% 1.45/1.65 (~b(elem!1, s(s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4908, 233, 809, 706, 272])).
% 1.45/1.65 tff(4910,plain,
% 1.45/1.65 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.65 tff(4911,plain,
% 1.45/1.65 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.45/1.65 inference(symmetry,[status(thm)],[4910])).
% 1.45/1.65 tff(4912,plain,
% 1.45/1.65 (b(s(z), s(elem!1))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[2854, 4911])).
% 1.45/1.65 tff(4913,plain,
% 1.45/1.65 ((s(z) = s(s(s(s(z))))) <=> (s(z) = s(elem!1))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1255])).
% 1.45/1.65 tff(4914,plain,
% 1.45/1.65 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(z) = s(elem!1)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4913])).
% 1.45/1.65 tff(4915,plain,
% 1.45/1.65 (~(s(z) = s(elem!1))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[67, 4914])).
% 1.45/1.65 tff(4916,plain,
% 1.45/1.65 (~(s(elem!1) = s(z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4915, 1481])).
% 1.45/1.65 tff(4917,plain,
% 1.45/1.65 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.65 tff(4918,plain,
% 1.45/1.65 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 1.45/1.65 inference(symmetry,[status(thm)],[4917])).
% 1.45/1.65 tff(4919,plain,
% 1.45/1.65 (r(s(elem!1), z)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[3244, 4918])).
% 1.45/1.65 tff(4920,plain,
% 1.45/1.65 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.65 tff(4921,plain,
% 1.45/1.65 (b(elem!1, s(z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[1072, 4920])).
% 1.45/1.65 tff(4922,plain,
% 1.45/1.65 (~b(s(z), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[975, 4921, 706, 809])).
% 1.45/1.65 tff(4923,plain,
% 1.45/1.65 (r(s(z), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[260, 4922])).
% 1.45/1.65 tff(4924,plain,
% 1.45/1.65 (r(z, s(s(s(z)))) <=> r(z, elem!1)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.65 tff(4925,plain,
% 1.45/1.65 (r(z, elem!1)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[97, 4924])).
% 1.45/1.65 tff(4926,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4927,plain,
% 1.45/1.65 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4928,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4927])).
% 1.45/1.65 tff(4929,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[4928, 4926])).
% 1.45/1.65 tff(4930,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(4931,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4930, 4929])).
% 1.45/1.65 tff(4932,plain,
% 1.45/1.65 ((~r(s(elem!1), s(z))) | (~r(s(elem!1), z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4931, 108, 4925, 4923])).
% 1.45/1.65 tff(4933,plain,
% 1.45/1.65 (~r(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4932, 4919])).
% 1.45/1.65 tff(4934,plain,
% 1.45/1.65 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1323, 45, 4933])).
% 1.45/1.65 tff(4935,plain,
% 1.45/1.65 (b(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4934, 4916])).
% 1.45/1.65 tff(4936,plain,
% 1.45/1.65 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.65 tff(4937,plain,
% 1.45/1.65 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 1.45/1.65 inference(symmetry,[status(thm)],[4936])).
% 1.45/1.65 tff(4938,plain,
% 1.45/1.65 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.65 tff(4939,plain,
% 1.45/1.65 (b(elem!1, s(s(s(s(z)))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[204, 4938])).
% 1.45/1.65 tff(4940,plain,
% 1.45/1.65 (b(elem!1, s(elem!1))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4939, 4937])).
% 1.45/1.65 tff(4941,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4942,plain,
% 1.45/1.65 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4943,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4942])).
% 1.45/1.65 tff(4944,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[4943, 4941])).
% 1.45/1.65 tff(4945,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(4946,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4945, 4944])).
% 1.45/1.65 tff(4947,plain,
% 1.45/1.65 (~b(s(z), s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4946, 233, 4940, 4921, 4935])).
% 1.45/1.65 tff(4948,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4947, 4912])).
% 1.45/1.65 tff(4949,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(4950,plain,
% 1.45/1.65 (~(s(s(s(z))) = elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4949, 809, 4810, 706, 2854, 1072, 204, 97])).
% 1.45/1.65 tff(4951,plain,
% 1.45/1.65 (~(elem!1 = s(s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1051, 4950])).
% 1.45/1.65 tff(4952,plain,
% 1.45/1.65 (r(elem!1, s(s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[886, 4951, 4909])).
% 1.45/1.65 tff(4953,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4954,plain,
% 1.45/1.65 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4955,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4954])).
% 1.45/1.65 tff(4956,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[4955, 4953])).
% 1.45/1.65 tff(4957,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(4958,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4957, 4956])).
% 1.45/1.65 tff(4959,plain,
% 1.45/1.65 (~b(s(s(s(z))), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4958, 233, 809, 706, 272])).
% 1.45/1.65 tff(4960,plain,
% 1.45/1.65 (r(s(s(s(z))), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[843, 4950, 4959])).
% 1.45/1.65 tff(4961,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[899, 108, 130, 4960, 780, 4952])).
% 1.45/1.65 tff(4962,plain,((~b(elem!1, z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(4963,plain,
% 1.45/1.65 (~b(elem!1, z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4962, 4902, 4307, 706, 2854, 1072, 204, 97, 272])).
% 1.45/1.65 tff(4964,plain,
% 1.45/1.65 (r(elem!1, z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1037, 4963, 1046])).
% 1.45/1.65 tff(4965,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4966,plain,
% 1.45/1.65 (((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4967,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4966])).
% 1.45/1.65 tff(4968,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[4967, 4965])).
% 1.45/1.65 tff(4969,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(4970,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4969, 4968])).
% 1.45/1.65 tff(4971,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4970, 108, 4964, 4902, 97, 4810])).
% 1.45/1.65 tff(4972,plain,((~b(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (elem!1 = z) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(4973,plain,
% 1.45/1.65 (~b(z, s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4972, 2854, 1046, 97, 1072, 204, 272, 4306, 828])).
% 1.45/1.65 tff(4974,plain,
% 1.45/1.65 (r(z, s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[357, 45, 4973, 352])).
% 1.45/1.65 tff(4975,plain,
% 1.45/1.65 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3276, 4974, 2240, 4809])).
% 1.45/1.65 tff(4976,plain,
% 1.45/1.65 (b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[462, 4975])).
% 1.45/1.65 tff(4977,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3384, 233, 4976, 204, 1072, 2854])).
% 1.45/1.65 tff(4978,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (elem!1 = z) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(4979,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4978, 4807, 2854, 2240, 1072, 1046, 97, 272, 4306, 204])).
% 1.45/1.65 tff(4980,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (elem!1 = z) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(4981,plain,
% 1.45/1.65 (~r(z, s(s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4980, 4330, 4328, 1632, 4305, 4318, 4306, 4806])).
% 1.45/1.65 tff(4982,plain,
% 1.45/1.65 (b(z, s(s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[78, 4981])).
% 1.45/1.65 tff(4983,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.45/1.65 tff(4984,plain,
% 1.45/1.65 (b(s(s(s(z))), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[843, 1049, 4983])).
% 1.45/1.65 tff(4985,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4986,plain,
% 1.45/1.65 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(4987,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[4986])).
% 1.45/1.65 tff(4988,plain,
% 1.45/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)))),
% 1.45/1.65 inference(transitivity,[status(thm)],[4987, 4985])).
% 1.45/1.65 tff(4989,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(4990,plain,
% 1.45/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[4989, 4988])).
% 1.45/1.65 tff(4991,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4990, 233, 809, 707, 273, 272])).
% 1.45/1.65 tff(4992,plain,((~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(4993,plain,
% 1.45/1.66 (~b(elem!1, z)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4992, 4984, 273, 272])).
% 1.45/1.66 tff(4994,plain,
% 1.45/1.66 (r(elem!1, z)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1037, 4993, 1632])).
% 1.45/1.66 tff(4995,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(4996,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(4997,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[4996, 4995])).
% 1.45/1.66 tff(4998,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4997, 108, 938, 1059, 701, 1213])).
% 1.45/1.66 tff(4999,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5000,plain,
% 1.45/1.66 (~r(z, elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4999, 4994, 1213, 701])).
% 1.45/1.66 tff(5001,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5002,plain,
% 1.45/1.66 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5003,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5002])).
% 1.45/1.66 tff(5004,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[5003, 5001])).
% 1.45/1.66 tff(5005,plain,
% 1.45/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(5006,plain,
% 1.45/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5005, 5004])).
% 1.45/1.66 tff(5007,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5006, 233, 921, 272, 1072, 402])).
% 1.45/1.66 tff(5008,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5009,plain,
% 1.45/1.66 (~b(s(z), z)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5008, 4347, 272, 1072])).
% 1.45/1.66 tff(5010,plain,
% 1.45/1.66 (r(s(z), z)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[260, 5009])).
% 1.45/1.66 tff(5011,plain,
% 1.45/1.66 (~b(elem!1, s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4355, 4347, 707, 272])).
% 1.45/1.66 tff(5012,plain,
% 1.45/1.66 (~b(s(s(z)), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4565, 5011, 701, 2848, 717, 284, 273, 707])).
% 1.45/1.66 tff(5013,plain,
% 1.45/1.66 (~(s(s(z)) = elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1687, 943])).
% 1.45/1.66 tff(5014,plain,
% 1.45/1.66 (~(elem!1 = s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1697, 5013])).
% 1.45/1.66 tff(5015,plain,
% 1.45/1.66 (~(elem!1 = s(s(s(s(z)))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[949, 943])).
% 1.45/1.66 tff(5016,plain,
% 1.45/1.66 (~(s(s(s(s(z)))) = elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[855, 5015])).
% 1.45/1.66 tff(5017,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[860, 5016, 828])).
% 1.45/1.66 tff(5018,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4520, 5017, 5014, 204, 284, 4359, 4424])).
% 1.45/1.66 tff(5019,plain,((~(s(z) = elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | b(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5020,plain,
% 1.45/1.66 (~(s(z) = elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5019, 5011, 284, 204, 5012, 4807])).
% 1.45/1.66 tff(5021,plain,
% 1.45/1.66 (~(elem!1 = s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[956, 5020])).
% 1.45/1.66 tff(5022,plain,
% 1.45/1.66 (r(elem!1, s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[965, 5021, 1653])).
% 1.45/1.66 tff(5023,plain,
% 1.45/1.66 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[792])).
% 1.45/1.66 tff(5024,plain,
% 1.45/1.66 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.45/1.66 inference(symmetry,[status(thm)],[5023])).
% 1.45/1.66 tff(5025,plain,
% 1.45/1.66 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5024])).
% 1.45/1.66 tff(5026,plain,
% 1.45/1.66 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.45/1.66 inference(symmetry,[status(thm)],[5025])).
% 1.45/1.66 tff(5027,plain,
% 1.45/1.66 (b(s(s(s(z))), s(elem!1))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2837, 5026])).
% 1.45/1.66 tff(5028,assumption,(~b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.45/1.66 tff(5029,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5028, 5027])).
% 1.45/1.66 tff(5030,plain,(b(s(s(s(z))), s(elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5031,plain,
% 1.45/1.66 (b(s(s(s(z))), s(elem!1))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5030, 792, 2837])).
% 1.45/1.66 tff(5032,plain,
% 1.45/1.66 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[792])).
% 1.45/1.66 tff(5033,plain,
% 1.45/1.66 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5032])).
% 1.45/1.66 tff(5034,plain,
% 1.45/1.66 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[576, 5033])).
% 1.45/1.66 tff(5035,plain,
% 1.45/1.66 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5024])).
% 1.45/1.66 tff(5036,plain,
% 1.45/1.66 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(elem!1), s(z))),
% 1.45/1.66 inference(symmetry,[status(thm)],[5035])).
% 1.45/1.66 tff(5037,plain,
% 1.45/1.66 ((s(s(s(s(s(z))))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5023])).
% 1.45/1.66 tff(5038,plain,
% 1.45/1.66 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(elem!1))),
% 1.45/1.66 inference(transitivity,[status(thm)],[5037, 1479])).
% 1.45/1.66 tff(5039,plain,
% 1.45/1.66 ((s(z) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.45/1.66 inference(symmetry,[status(thm)],[5038])).
% 1.45/1.66 tff(5040,plain,
% 1.45/1.66 ((~(s(z) = s(elem!1))) <=> (~(s(s(s(s(s(z))))) = s(z)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5039])).
% 1.45/1.66 tff(5041,plain,
% 1.45/1.66 (~(s(s(s(s(s(z))))) = s(z))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[1309, 5040])).
% 1.45/1.66 tff(5042,plain,
% 1.45/1.66 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(elem!1), s(z))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5023])).
% 1.45/1.66 tff(5043,plain,
% 1.45/1.66 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.66 inference(symmetry,[status(thm)],[5042])).
% 1.45/1.66 tff(5044,plain,
% 1.45/1.66 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(s(s(z))))), s(z)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5043])).
% 1.45/1.66 tff(5045,plain,
% 1.45/1.66 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[792])).
% 1.45/1.66 tff(5046,plain,
% 1.45/1.66 (b(s(z), elem!1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[2854, 5045])).
% 1.45/1.66 tff(5047,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.45/1.66 tff(5048,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5049,plain,
% 1.45/1.66 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5050,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5049])).
% 1.45/1.66 tff(5051,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[5050, 5048])).
% 1.45/1.66 tff(5052,plain,
% 1.45/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(5053,plain,
% 1.45/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5052, 5051])).
% 1.45/1.66 tff(5054,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5053, 233, 1102, 1072, 1327, 5047])).
% 1.45/1.66 tff(5055,plain,((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5056,plain,
% 1.45/1.66 (~b(s(elem!1), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5055, 5046, 1072, 5031])).
% 1.45/1.66 tff(5057,plain,
% 1.45/1.66 (~b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5056, 5044])).
% 1.45/1.66 tff(5058,plain,
% 1.45/1.66 (r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[556, 5057, 5041])).
% 1.45/1.66 tff(5059,plain,
% 1.45/1.66 (r(s(elem!1), s(z))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5058, 5036])).
% 1.45/1.66 tff(5060,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5061,plain,
% 1.45/1.66 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5062,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5061])).
% 1.45/1.66 tff(5063,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[5062, 5060])).
% 1.45/1.66 tff(5064,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(5065,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5064, 5063])).
% 1.45/1.66 tff(5066,plain,
% 1.45/1.66 (~r(s(elem!1), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5065, 108, 1389, 246, 5059])).
% 1.45/1.66 tff(5067,plain,
% 1.45/1.66 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5023])).
% 1.45/1.66 tff(5068,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.45/1.66 tff(5069,plain,
% 1.45/1.66 (r(s(elem!1), elem!1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5068, 5067])).
% 1.45/1.66 tff(5070,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.45/1.66 tff(5071,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5070, 5069])).
% 1.45/1.66 tff(5072,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(elem!1), elem!1) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5073,plain,
% 1.45/1.66 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5072, 5066, 792])).
% 1.45/1.66 tff(5074,plain,
% 1.45/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5075,plain,
% 1.45/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(5076,plain,
% 1.45/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5075, 5074])).
% 1.45/1.66 tff(5077,plain,
% 1.45/1.66 ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5076, 45])).
% 1.45/1.66 tff(5078,plain,
% 1.45/1.66 (b(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5077, 5073, 5034])).
% 1.45/1.66 tff(5079,plain,
% 1.45/1.66 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5024])).
% 1.45/1.66 tff(5080,plain,
% 1.45/1.66 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.45/1.66 inference(symmetry,[status(thm)],[5079])).
% 1.45/1.66 tff(5081,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.45/1.66 tff(5082,plain,
% 1.45/1.66 (b(s(elem!1), elem!1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5081, 5080])).
% 1.45/1.66 tff(5083,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.45/1.66 tff(5084,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5083, 5082])).
% 1.45/1.66 tff(5085,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(elem!1), elem!1) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5086,plain,
% 1.45/1.66 (b(s(elem!1), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5085, 5078, 792])).
% 1.45/1.66 tff(5087,plain,
% 1.45/1.66 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5024])).
% 1.45/1.66 tff(5088,plain,
% 1.45/1.66 ((elem!1 = s(elem!1)) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.45/1.66 inference(transitivity,[status(thm)],[5087, 1254])).
% 1.45/1.66 tff(5089,plain,
% 1.45/1.66 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.45/1.66 inference(symmetry,[status(thm)],[5088])).
% 1.45/1.66 tff(5090,plain,
% 1.45/1.66 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(elem!1 = s(elem!1)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5089])).
% 1.45/1.66 tff(5091,plain,
% 1.45/1.66 (~(elem!1 = s(elem!1))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5034, 5090])).
% 1.45/1.66 tff(5092,plain,
% 1.45/1.66 (r(s(elem!1), s(z))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[747, 5036])).
% 1.45/1.66 tff(5093,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5094,plain,
% 1.45/1.66 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5095,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5094])).
% 1.45/1.66 tff(5096,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[5095, 5093])).
% 1.45/1.66 tff(5097,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(5098,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5097, 5096])).
% 1.45/1.66 tff(5099,plain,
% 1.45/1.66 (~r(s(elem!1), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5098, 108, 1498, 1389, 246])).
% 1.45/1.66 tff(5100,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5099, 5092])).
% 1.45/1.66 tff(5101,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5102,plain,
% 1.45/1.66 (~r(elem!1, s(elem!1))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5101, 5058, 792, 1389, 246])).
% 1.45/1.66 tff(5103,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.45/1.66 tff(5104,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.45/1.66 tff(5105,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.45/1.66 tff(5106,plain,
% 1.45/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5107,plain,
% 1.45/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(5108,plain,
% 1.45/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5107, 5106])).
% 1.45/1.66 tff(5109,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5108, 45, 5105, 5104, 5103])).
% 1.45/1.66 tff(5110,plain,(r(elem!1, s(elem!1)) | b(elem!1, s(elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5111,plain,
% 1.45/1.66 (b(elem!1, s(elem!1))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5110, 5102, 5091])).
% 1.45/1.66 tff(5112,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5113,plain,
% 1.45/1.66 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5114,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5113])).
% 1.45/1.66 tff(5115,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[5114, 5112])).
% 1.45/1.66 tff(5116,plain,
% 1.45/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(z))), elem!1)))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(5117,plain,
% 1.45/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[5116, 5115])).
% 1.45/1.66 tff(5118,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5117, 233, 707, 5111, 5086, 5031])).
% 1.45/1.66 tff(5119,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (s(z) = s(elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5120,plain,
% 1.45/1.66 (~(s(s(s(s(z)))) = elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5119, 5022, 707, 5010, 1072, 2837, 726, 2854])).
% 1.45/1.66 tff(5121,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[860, 5120, 4807])).
% 1.45/1.66 tff(5122,plain,
% 1.45/1.66 (~r(elem!1, s(s(s(z))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4787, 5121, 491, 1213])).
% 1.45/1.66 tff(5123,plain,
% 1.45/1.66 (b(elem!1, s(s(s(z))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[886, 5122, 836])).
% 1.45/1.66 tff(5124,plain,
% 1.45/1.66 (elem!1 = s(s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4520, 5121, 204, 284, 5011, 5012])).
% 1.45/1.66 tff(5125,plain,
% 1.45/1.66 (s(s(z)) = elem!1),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1697, 5124])).
% 1.45/1.66 tff(5126,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4767, 5125, 5123, 4303])).
% 1.45/1.66 tff(5127,plain,(r(z, elem!1) | b(s(s(z)), s(s(s(z)))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | b(elem!1, s(z)) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (z = elem!1) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(5128,plain,
% 1.45/1.66 (b(elem!1, s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5127, 5000, 4764, 204, 284, 491, 1213, 4984, 1072, 2837, 2854, 4303, 272, 701, 717, 273])).
% 1.45/1.66 tff(5129,plain,
% 1.45/1.66 (b(z, elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[934, 5000, 717])).
% 1.45/1.66 tff(5130,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5131,plain,
% 1.45/1.66 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(5132,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[5131])).
% 1.45/1.66 tff(5133,plain,
% 1.45/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[5132, 5130])).
% 1.45/1.66 tff(5134,plain,
% 1.45/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(5135,plain,
% 1.45/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, s(z)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5134, 5133])).
% 1.45/1.67 tff(5136,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5135, 233, 5129, 4984, 273, 5128])).
% 1.45/1.67 tff(5137,plain,((s(s(s(z))) = elem!1) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (z = elem!1) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5138,plain,
% 1.45/1.67 (s(s(s(z))) = elem!1),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5137, 4982, 4806, 284, 491, 4804, 4328, 4340, 4330, 4303, 4318, 4304, 717, 4316])).
% 1.45/1.67 tff(5139,plain,
% 1.45/1.67 (b(s(s(s(z))), elem!1) <=> b(elem!1, elem!1)),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5138])).
% 1.45/1.67 tff(5140,plain,
% 1.45/1.67 (b(elem!1, elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.45/1.67 inference(symmetry,[status(thm)],[5139])).
% 1.45/1.67 tff(5141,plain,
% 1.45/1.67 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5140])).
% 1.45/1.67 tff(5142,plain,
% 1.45/1.67 (~b(s(s(s(z))), elem!1)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[4762, 5141])).
% 1.45/1.67 tff(5143,plain,
% 1.45/1.67 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4823, 834, 4306])).
% 1.45/1.67 tff(5144,plain,
% 1.45/1.67 (r(s(elem!1), elem!1)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5143, 4420])).
% 1.45/1.67 tff(5145,plain,
% 1.45/1.67 (~r(s(s(s(z))), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4326, 4307, 2240, 491])).
% 1.45/1.67 tff(5146,plain,
% 1.45/1.67 (b(s(s(s(z))), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1090, 5145])).
% 1.45/1.67 tff(5147,plain,
% 1.45/1.67 (b(elem!1, s(z))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5146, 4920])).
% 1.45/1.67 tff(5148,plain,
% 1.45/1.67 (~r(elem!1, s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4451, 5143, 491, 1213])).
% 1.45/1.67 tff(5149,plain,
% 1.45/1.67 (b(elem!1, s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1236, 5148, 4505])).
% 1.45/1.67 tff(5150,plain,
% 1.45/1.67 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.67 tff(5151,plain,
% 1.45/1.67 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(elem!1))),
% 1.45/1.67 inference(symmetry,[status(thm)],[5150])).
% 1.45/1.67 tff(5152,plain,
% 1.45/1.67 (r(s(s(z)), s(elem!1))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[491, 5151])).
% 1.45/1.67 tff(5153,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.45/1.67 tff(5154,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5155,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(5156,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5155, 5154])).
% 1.45/1.67 tff(5157,plain,
% 1.45/1.67 ((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5156, 108, 5153, 1497])).
% 1.45/1.67 tff(5158,plain,
% 1.45/1.67 (~r(s(s(z)), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5157, 5152])).
% 1.45/1.67 tff(5159,plain,
% 1.45/1.67 (b(s(s(z)), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[48, 45, 35, 5158])).
% 1.45/1.67 tff(5160,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5161,plain,
% 1.45/1.67 (((~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5162,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5161])).
% 1.45/1.67 tff(5163,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[5162, 5160])).
% 1.45/1.67 tff(5164,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(z)))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(5165,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(z)), s(elem!1)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 1.45/1.67 tff(5166,plain,
% 1.45/1.67 ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5165, 108, 5153, 1497])).
% 1.45/1.67 tff(5167,plain,
% 1.45/1.67 (~r(s(z), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5166, 5152])).
% 1.45/1.67 tff(5168,plain,
% 1.45/1.67 (b(s(z), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[481, 45, 34, 5167])).
% 1.45/1.67 tff(5169,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5170,plain,
% 1.45/1.67 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5171,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5170])).
% 1.45/1.67 tff(5172,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[5171, 5169])).
% 1.45/1.67 tff(5173,plain,
% 1.45/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(5174,plain,
% 1.45/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5173, 5172])).
% 1.45/1.67 tff(5175,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5174, 233, 1009, 5168, 967, 5159])).
% 1.45/1.67 tff(5176,plain,((~r(s(z), s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5177,plain,
% 1.45/1.67 (~r(s(z), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5176, 5149, 5147, 5144, 491, 834])).
% 1.45/1.67 tff(5178,plain,
% 1.45/1.67 (~r(s(z), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1494, 5177, 834])).
% 1.45/1.67 tff(5179,plain,
% 1.45/1.67 (b(s(z), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1122, 5178])).
% 1.45/1.67 tff(5180,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.45/1.67 tff(5181,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5180, 4912])).
% 1.45/1.67 tff(5182,plain,(b(s(z), s(elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5183,plain,
% 1.45/1.67 (b(s(z), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5182, 5179, 834])).
% 1.45/1.67 tff(5184,plain,
% 1.45/1.67 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1256])).
% 1.45/1.67 tff(5185,plain,
% 1.45/1.67 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[5184, 4684])).
% 1.45/1.67 tff(5186,plain,
% 1.45/1.67 ((s(z) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.45/1.67 inference(symmetry,[status(thm)],[5185])).
% 1.45/1.67 tff(5187,plain,
% 1.45/1.67 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(z)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5186])).
% 1.45/1.67 tff(5188,plain,
% 1.45/1.67 (~(s(s(s(s(s(z))))) = s(z))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[1348, 5187])).
% 1.45/1.67 tff(5189,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 1.45/1.67 tff(5190,plain,
% 1.45/1.67 (s(s(s(z))) = s(elem!1)),
% 1.45/1.67 inference(symmetry,[status(thm)],[5189])).
% 1.45/1.67 tff(5191,plain,
% 1.45/1.67 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5190])).
% 1.45/1.67 tff(5192,plain,
% 1.45/1.67 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.45/1.67 inference(symmetry,[status(thm)],[5191])).
% 1.45/1.67 tff(5193,plain,
% 1.45/1.67 (elem!1 = inj_0(s(elem!1))),
% 1.45/1.67 inference(symmetry,[status(thm)],[719])).
% 1.45/1.67 tff(5194,plain,
% 1.45/1.67 (elem!1 = s(s(z))),
% 1.45/1.67 inference(transitivity,[status(thm)],[5193, 5192, 164])).
% 1.45/1.67 tff(5195,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4505, 5194])).
% 1.45/1.67 tff(5196,plain,((~(s(elem!1) = s(s(s(z))))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5197,plain,
% 1.45/1.67 (~(s(elem!1) = s(s(s(z))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5196, 4505])).
% 1.45/1.67 tff(5198,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 1.45/1.67 tff(5199,plain,
% 1.45/1.67 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5198])).
% 1.45/1.67 tff(5200,plain,
% 1.45/1.67 (s(elem!1) = s(s(s(z)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[1343, 5199, 61])).
% 1.45/1.67 tff(5201,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.45/1.67 tff(5202,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5201, 5200])).
% 1.45/1.67 tff(5203,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (s(elem!1) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5204,plain,
% 1.45/1.67 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5203, 5197])).
% 1.45/1.67 tff(5205,plain,
% 1.45/1.67 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(elem!1)))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1256])).
% 1.45/1.67 tff(5206,plain,
% 1.45/1.67 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.67 tff(5207,plain,
% 1.45/1.67 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4338, 4307, 2240, 491])).
% 1.45/1.67 tff(5208,plain,
% 1.45/1.67 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[759, 5207])).
% 1.45/1.67 tff(5209,plain,
% 1.45/1.67 (b(elem!1, s(s(s(s(s(z))))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5208, 5206])).
% 1.45/1.67 tff(5210,plain,
% 1.45/1.67 (b(elem!1, s(s(elem!1)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5209, 5205])).
% 1.45/1.67 tff(5211,plain,
% 1.45/1.67 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 1.45/1.67 inference(monotonicity,[status(thm)],[834])).
% 1.45/1.67 tff(5212,plain,
% 1.45/1.67 (~r(s(s(s(z))), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2586, 4307, 2240, 491])).
% 1.45/1.67 tff(5213,plain,
% 1.45/1.67 (b(s(s(s(z))), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[244, 5212])).
% 1.45/1.67 tff(5214,plain,
% 1.45/1.67 (b(elem!1, z)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5213, 5211])).
% 1.45/1.67 tff(5215,plain,
% 1.45/1.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2598, 4307, 2240, 491])).
% 1.45/1.67 tff(5216,plain,
% 1.45/1.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[186, 5215])).
% 1.45/1.67 tff(5217,plain,
% 1.45/1.67 (~r(z, s(s(s(z))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4980, 5179, 5146, 1046, 2240, 5213, 4306, 5216])).
% 1.45/1.67 tff(5218,plain,
% 1.45/1.67 (b(z, s(s(s(z))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[78, 5217])).
% 1.45/1.67 tff(5219,plain,
% 1.45/1.67 (b(z, elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1030, 5218, 834])).
% 1.45/1.67 tff(5220,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[1362])).
% 1.45/1.67 tff(5221,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.45/1.67 inference(symmetry,[status(thm)],[5220])).
% 1.45/1.67 tff(5222,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 1.45/1.67 tff(5223,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.45/1.67 tff(5224,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5225,plain,
% 1.45/1.67 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5226,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5225])).
% 1.45/1.67 tff(5227,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[5226, 5224])).
% 1.45/1.67 tff(5228,plain,
% 1.45/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(5229,plain,
% 1.45/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5228, 5227])).
% 1.45/1.67 tff(5230,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5229, 233, 1290, 967, 1328, 5223])).
% 1.45/1.67 tff(5231,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5232,plain,
% 1.45/1.67 (~b(s(s(elem!1)), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5231, 1328, 967, 1290])).
% 1.45/1.67 tff(5233,plain,
% 1.45/1.67 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1417, 5232, 834])).
% 1.45/1.67 tff(5234,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1409, 5233, 5222])).
% 1.45/1.67 tff(5235,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(elem!1))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5234, 5221])).
% 1.45/1.67 tff(5236,plain,
% 1.45/1.67 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1794, 1328, 967, 1290])).
% 1.45/1.67 tff(5237,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1616, 45, 5236, 1380])).
% 1.45/1.67 tff(5238,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.45/1.67 tff(5239,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5240,plain,
% 1.45/1.67 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5241,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5240])).
% 1.45/1.67 tff(5242,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[5241, 5239])).
% 1.45/1.67 tff(5243,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(5244,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 1.45/1.67 tff(5245,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5244, 108, 5153, 5238, 1575, 1386])).
% 1.45/1.67 tff(5246,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5247,plain,
% 1.45/1.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5246, 5237, 5153, 5235])).
% 1.45/1.67 tff(5248,plain,
% 1.45/1.67 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1593, 5247, 834])).
% 1.45/1.67 tff(5249,plain,
% 1.45/1.67 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1598, 5248, 1377])).
% 1.45/1.67 tff(5250,plain,
% 1.45/1.67 (b(s(s(s(elem!1))), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1605, 5249, 834])).
% 1.45/1.67 tff(5251,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5252,plain,
% 1.45/1.67 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5253,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[5252])).
% 1.45/1.67 tff(5254,plain,
% 1.45/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[5253, 5251])).
% 1.45/1.67 tff(5255,plain,
% 1.45/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(5256,plain,
% 1.45/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[5255, 5254])).
% 1.45/1.67 tff(5257,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5256, 233, 921, 809, 967, 402])).
% 1.45/1.67 tff(5258,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(5259,plain,
% 1.45/1.67 (~b(s(z), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5258, 921, 809, 967])).
% 1.45/1.67 tff(5260,plain,
% 1.45/1.67 (r(s(z), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[260, 5259])).
% 1.45/1.67 tff(5261,assumption,(r(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.45/1.67 tff(5262,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(5263,plain,
% 1.45/1.68 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5264,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5263])).
% 1.45/1.68 tff(5265,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[5264, 5262])).
% 1.45/1.68 tff(5266,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5267,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), s(elem!1)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5266, 5265])).
% 1.45/1.68 tff(5268,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5267, 108, 1213, 5153, 1577, 5261])).
% 1.45/1.68 tff(5269,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(5270,plain,
% 1.45/1.68 (~r(elem!1, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5269, 5152, 5153, 1213])).
% 1.45/1.68 tff(5271,plain,
% 1.45/1.68 (b(elem!1, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1473, 5270, 1456])).
% 1.45/1.68 tff(5272,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.45/1.68 tff(5273,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.45/1.68 tff(5274,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5275,plain,
% 1.45/1.68 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5276,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5275])).
% 1.45/1.68 tff(5277,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[5276, 5274])).
% 1.45/1.68 tff(5278,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5279,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5278, 5277])).
% 1.45/1.68 tff(5280,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5279, 233, 921, 1460, 5273, 5272])).
% 1.45/1.68 tff(5281,plain,((~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(5282,plain,
% 1.45/1.68 (~b(z, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5281, 5271, 921, 5250])).
% 1.45/1.68 tff(5283,plain,
% 1.45/1.68 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.45/1.68 inference(commutativity,[status(thm)],[])).
% 1.45/1.68 tff(5284,plain,
% 1.45/1.68 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.45/1.68 inference(symmetry,[status(thm)],[5283])).
% 1.45/1.68 tff(5285,plain,
% 1.45/1.68 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5284])).
% 1.45/1.68 tff(5286,plain,
% 1.45/1.68 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5287,plain,
% 1.45/1.68 (~(s(s(s(elem!1))) = z)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5286, 30])).
% 1.45/1.68 tff(5288,plain,
% 1.45/1.68 (~(z = s(s(s(elem!1))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5287, 5285])).
% 1.45/1.68 tff(5289,plain,
% 1.45/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5290,plain,
% 1.45/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5291,plain,
% 1.45/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 1.45/1.68 tff(5292,plain,
% 1.45/1.68 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5291, 45])).
% 1.45/1.68 tff(5293,plain,
% 1.45/1.68 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5292, 5288])).
% 1.45/1.68 tff(5294,plain,
% 1.45/1.68 (r(z, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5293, 5282])).
% 1.45/1.68 tff(5295,plain,
% 1.45/1.68 ((elem!1 = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.45/1.68 inference(commutativity,[status(thm)],[])).
% 1.45/1.68 tff(5296,plain,
% 1.45/1.68 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[1256])).
% 1.45/1.68 tff(5297,plain,
% 1.45/1.68 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.45/1.68 inference(symmetry,[status(thm)],[5296])).
% 1.45/1.68 tff(5298,plain,
% 1.45/1.68 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5297])).
% 1.45/1.68 tff(5299,plain,
% 1.45/1.68 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.45/1.68 inference(transitivity,[status(thm)],[5298, 5295])).
% 1.45/1.68 tff(5300,plain,
% 1.45/1.68 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5299])).
% 1.45/1.68 tff(5301,plain,
% 1.45/1.68 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1456, 5300])).
% 1.45/1.68 tff(5302,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.45/1.68 tff(5303,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.45/1.68 tff(5304,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5305,plain,
% 1.45/1.68 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5306,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5305])).
% 1.45/1.68 tff(5307,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[5306, 5304])).
% 1.45/1.68 tff(5308,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5309,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5308, 5307])).
% 1.45/1.68 tff(5310,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5309, 108, 5303, 5302, 1576, 246])).
% 1.45/1.68 tff(5311,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(5312,plain,
% 1.45/1.68 (~r(s(s(s(elem!1))), elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5311, 1576, 5302, 246])).
% 1.45/1.68 tff(5313,plain,
% 1.45/1.68 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5297])).
% 1.45/1.68 tff(5314,plain,
% 1.45/1.68 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.45/1.68 inference(symmetry,[status(thm)],[5313])).
% 1.45/1.68 tff(5315,assumption,(r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.45/1.68 tff(5316,plain,
% 1.45/1.68 (r(s(s(s(elem!1))), elem!1)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5315, 5314])).
% 1.45/1.68 tff(5317,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.45/1.68 tff(5318,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5317, 5316])).
% 1.45/1.68 tff(5319,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(5320,plain,
% 1.45/1.68 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5319, 5312, 834])).
% 1.45/1.68 tff(5321,plain,
% 1.45/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5322,plain,
% 1.45/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5323,plain,
% 1.45/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5322, 5321])).
% 1.45/1.68 tff(5324,plain,
% 1.45/1.68 ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5323, 45])).
% 1.45/1.68 tff(5325,plain,
% 1.45/1.68 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5324, 5320, 5301])).
% 1.45/1.68 tff(5326,plain,
% 1.45/1.68 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5297])).
% 1.45/1.68 tff(5327,plain,
% 1.45/1.68 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.45/1.68 inference(symmetry,[status(thm)],[5326])).
% 1.45/1.68 tff(5328,assumption,(b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.45/1.68 tff(5329,plain,
% 1.45/1.68 (b(s(s(s(elem!1))), elem!1)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 1.45/1.68 tff(5330,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.45/1.68 tff(5331,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5330, 5329])).
% 1.45/1.68 tff(5332,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | b(s(s(s(elem!1))), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(5333,plain,
% 1.45/1.68 (b(s(s(s(elem!1))), elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5332, 5325, 834])).
% 1.45/1.68 tff(5334,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5335,plain,
% 1.45/1.68 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5336,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5335])).
% 1.45/1.68 tff(5337,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[5336, 5334])).
% 1.45/1.68 tff(5338,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5339,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 1.45/1.68 tff(5340,plain,
% 1.45/1.68 (~b(s(s(s(elem!1))), z)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5339, 233, 921, 809, 5333])).
% 1.45/1.68 tff(5341,plain,
% 1.45/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5342,plain,
% 1.45/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5343,plain,
% 1.45/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5342, 5341])).
% 1.45/1.68 tff(5344,plain,
% 1.45/1.68 (r(s(s(s(elem!1))), z)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5343, 45, 5287, 5340])).
% 1.45/1.68 tff(5345,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5346,plain,
% 1.45/1.68 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5347,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5346])).
% 1.45/1.68 tff(5348,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[5347, 5345])).
% 1.45/1.68 tff(5349,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5350,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5349, 5348])).
% 1.45/1.68 tff(5351,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5350, 108, 5302, 1576, 246, 5344])).
% 1.45/1.68 tff(5352,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(5353,plain,
% 1.45/1.68 (~r(s(z), s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5352, 5294, 5260, 921, 809, 834])).
% 1.45/1.68 tff(5354,plain,
% 1.45/1.68 (b(s(z), s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1441, 5353])).
% 1.45/1.68 tff(5355,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5356,plain,
% 1.45/1.68 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5357,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5356])).
% 1.45/1.68 tff(5358,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[5357, 5355])).
% 1.45/1.68 tff(5359,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5360,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 1.45/1.68 tff(5361,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5360, 233, 5271, 967, 5354, 5250])).
% 1.45/1.68 tff(5362,plain,((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(s(s(z))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(5363,plain,
% 1.45/1.68 (~b(s(z), s(s(elem!1)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5362, 5147, 5219, 5214, 834, 5144, 1213, 5210, 491, 5204])).
% 1.45/1.68 tff(5364,plain,
% 1.45/1.68 (r(s(z), s(s(elem!1)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1352, 5363])).
% 1.45/1.68 tff(5365,plain,
% 1.45/1.68 (b(elem!1, s(s(s(s(z)))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5216, 4938])).
% 1.45/1.68 tff(5366,plain,
% 1.45/1.68 (b(elem!1, s(elem!1))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5365, 4937])).
% 1.45/1.68 tff(5367,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.45/1.68 tff(5368,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.45/1.68 tff(5369,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5370,plain,
% 1.45/1.68 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(5371,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5370])).
% 1.45/1.68 tff(5372,plain,
% 1.45/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[5371, 5369])).
% 1.45/1.68 tff(5373,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(5374,plain,
% 1.45/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[5373, 5372])).
% 1.45/1.68 tff(5375,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[5374, 233, 5368, 967, 1287, 5367])).
% 1.45/1.69 tff(5376,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5377,plain,
% 1.45/1.69 (~b(s(elem!1), s(s(elem!1)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5376, 5366, 5147, 5183])).
% 1.45/1.69 tff(5378,plain,
% 1.45/1.69 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1277, 5377, 834])).
% 1.45/1.69 tff(5379,plain,
% 1.45/1.69 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[745, 5378])).
% 1.45/1.69 tff(5380,plain,
% 1.45/1.69 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1255, 1256])).
% 1.45/1.69 tff(5381,plain,
% 1.45/1.69 (r(s(elem!1), s(s(elem!1)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[727, 5380])).
% 1.45/1.69 tff(5382,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.45/1.69 tff(5383,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5382, 5381])).
% 1.45/1.69 tff(5384,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | r(s(elem!1), s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5385,plain,
% 1.45/1.69 (r(s(elem!1), s(s(elem!1)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5384, 5379, 834])).
% 1.45/1.69 tff(5386,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.45/1.69 tff(5387,plain,
% 1.45/1.69 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1257])).
% 1.45/1.69 tff(5388,plain,
% 1.45/1.69 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.45/1.69 inference(symmetry,[status(thm)],[5387])).
% 1.45/1.69 tff(5389,plain,
% 1.45/1.69 (r(s(s(elem!1)), s(z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[747, 5388])).
% 1.45/1.69 tff(5390,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5391,plain,
% 1.45/1.69 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5392,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[5391])).
% 1.45/1.69 tff(5393,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[5392, 5390])).
% 1.45/1.69 tff(5394,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(5395,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5394, 5393])).
% 1.45/1.69 tff(5396,plain,
% 1.45/1.69 (~r(s(s(elem!1)), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5395, 108, 1388, 5386, 1497])).
% 1.45/1.69 tff(5397,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5396, 5389])).
% 1.45/1.69 tff(5398,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5399,plain,
% 1.45/1.69 (~r(s(z), s(elem!1))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5398, 747, 5386, 1388, 834])).
% 1.45/1.69 tff(5400,plain,
% 1.45/1.69 (~r(s(z), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1494, 5399, 834])).
% 1.45/1.69 tff(5401,plain,
% 1.45/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1122, 5400])).
% 1.45/1.69 tff(5402,plain,
% 1.45/1.69 (b(s(z), s(elem!1))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5401, 4911])).
% 1.45/1.69 tff(5403,plain,
% 1.45/1.69 (r(s(s(elem!1)), s(z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[747, 1476])).
% 1.45/1.69 tff(5404,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5405,plain,
% 1.45/1.69 (((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5406,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[5405])).
% 1.45/1.69 tff(5407,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[5406, 5404])).
% 1.45/1.69 tff(5408,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(5409,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5408, 5407])).
% 1.45/1.69 tff(5410,plain,
% 1.45/1.69 (~r(s(elem!1), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5409, 108, 1388, 5386, 5403])).
% 1.45/1.69 tff(5411,plain,
% 1.45/1.69 ((s(elem!1) = s(z)) | b(s(elem!1), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1323, 45, 5410])).
% 1.45/1.69 tff(5412,plain,
% 1.45/1.69 (b(s(elem!1), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5411, 1482])).
% 1.45/1.69 tff(5413,plain,
% 1.45/1.69 (~b(s(z), s(elem!1))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[4946, 233, 5368, 967, 5412])).
% 1.45/1.69 tff(5414,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5413, 5402])).
% 1.45/1.69 tff(5415,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5416,plain,
% 1.45/1.69 (~r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5415, 5385, 5366, 5147, 1309, 5364, 834])).
% 1.45/1.69 tff(5417,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[556, 5416, 5188])).
% 1.45/1.69 tff(5418,plain,
% 1.45/1.69 (b(s(s(elem!1)), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1283, 5417, 834])).
% 1.45/1.69 tff(5419,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5420,plain,
% 1.45/1.69 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5421,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[5420])).
% 1.45/1.69 tff(5422,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[5421, 5419])).
% 1.45/1.69 tff(5423,plain,
% 1.45/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(5424,plain,
% 1.45/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 1.45/1.69 tff(5425,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5424, 233, 5210, 5147, 5418, 5183])).
% 1.45/1.69 tff(5426,plain,((~(s(s(s(z))) = elem!1)) | (s(z) = s(elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | (~r(s(s(z)), s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5427,plain,
% 1.45/1.69 (elem!1 = s(s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5426, 5138, 4804, 491, 1632, 4305, 4306, 726])).
% 1.45/1.69 tff(5428,plain,
% 1.45/1.69 (s(s(z)) = elem!1),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1697, 5427])).
% 1.45/1.69 tff(5429,plain,
% 1.45/1.69 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1677])).
% 1.45/1.69 tff(5430,plain,
% 1.45/1.69 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 1.45/1.69 inference(symmetry,[status(thm)],[5429])).
% 1.45/1.69 tff(5431,plain,
% 1.45/1.69 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(z))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[5430])).
% 1.45/1.69 tff(5432,plain,
% 1.45/1.69 (~b(s(s(s(z))), s(s(z)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[797, 5431])).
% 1.45/1.69 tff(5433,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[284, 5432])).
% 1.45/1.69 tff(5434,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5435,plain,
% 1.45/1.69 (b(s(s(s(z))), elem!1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5434, 5428, 284])).
% 1.45/1.69 tff(5436,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5435, 5142])).
% 1.45/1.69 tff(5437,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z)))) | (z = elem!1) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5438,plain,
% 1.45/1.69 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5437, 491, 284, 4303, 717, 3244, 368])).
% 1.45/1.69 tff(5439,plain,
% 1.45/1.69 (~r(z, s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[4008, 491, 4304, 3244])).
% 1.45/1.69 tff(5440,plain,
% 1.45/1.69 (b(z, s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[220, 45, 5439, 215])).
% 1.45/1.69 tff(5441,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5442,plain,
% 1.45/1.69 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5443,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[5442])).
% 1.45/1.69 tff(5444,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[5443, 5441])).
% 1.45/1.69 tff(5445,plain,
% 1.45/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(5446,plain,
% 1.45/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5445, 5444])).
% 1.45/1.69 tff(5447,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5446, 233, 389, 284, 273, 1930])).
% 1.45/1.69 tff(5448,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5449,plain,
% 1.45/1.69 (~b(z, s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5448, 5440, 284, 5438])).
% 1.45/1.69 tff(5450,plain,
% 1.45/1.69 (r(z, s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[78, 5449])).
% 1.45/1.69 tff(5451,plain,
% 1.45/1.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2612, 5450, 4305, 4304])).
% 1.45/1.69 tff(5452,plain,
% 1.45/1.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[186, 5451])).
% 1.45/1.69 tff(5453,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5454,plain,
% 1.45/1.69 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5455,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[5454])).
% 1.45/1.69 tff(5456,plain,
% 1.45/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[5455, 5453])).
% 1.45/1.69 tff(5457,plain,
% 1.45/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(5458,plain,
% 1.45/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5457, 5456])).
% 1.45/1.69 tff(5459,plain,
% 1.45/1.69 (~b(s(s(s(z))), z)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5458, 233, 5438, 5440, 5452])).
% 1.45/1.69 tff(5460,plain,
% 1.45/1.69 (r(s(s(s(z))), z)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[244, 5459])).
% 1.45/1.69 tff(5461,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2622, 108, 4304, 4305, 5450, 5460])).
% 1.45/1.69 tff(5462,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z)))) | (z = elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5463,plain,
% 1.45/1.69 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5462, 368, 3244, 4303, 717, 284])).
% 1.45/1.69 tff(5464,plain,
% 1.45/1.69 (b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[440, 5463])).
% 1.45/1.69 tff(5465,plain,
% 1.45/1.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2612, 79, 4305, 4304])).
% 1.45/1.69 tff(5466,plain,
% 1.45/1.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[186, 5465])).
% 1.45/1.69 tff(5467,plain,
% 1.45/1.69 (~r(s(s(s(z))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2648, 79, 4305, 4304])).
% 1.45/1.69 tff(5468,plain,
% 1.45/1.69 (b(s(s(s(z))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1090, 5467])).
% 1.45/1.69 tff(5469,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5470,plain,
% 1.45/1.69 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5471,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[5470])).
% 1.45/1.69 tff(5472,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[5471, 5469])).
% 1.45/1.69 tff(5473,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(5474,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 1.45/1.69 tff(5475,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5474, 108, 493, 247, 81, 3244])).
% 1.45/1.69 tff(5476,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(5477,plain,
% 1.45/1.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5476, 493, 3244, 247])).
% 1.45/1.69 tff(5478,plain,
% 1.45/1.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[186, 5477])).
% 1.45/1.69 tff(5479,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(5480,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.70 inference(quant_inst,[status(thm)],[])).
% 1.45/1.70 tff(5481,plain,
% 1.45/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.45/1.70 inference(modus_ponens,[status(thm)],[5480, 5479])).
% 1.45/1.70 tff(5482,plain,
% 1.45/1.70 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[5481, 108, 493, 247, 3244])).
% 1.45/1.70 tff(5483,plain,
% 1.45/1.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[386, 5482])).
% 1.45/1.70 tff(5484,plain,
% 1.45/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(5485,plain,
% 1.45/1.70 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.70 inference(rewrite,[status(thm)],[])).
% 1.45/1.70 tff(5486,plain,
% 1.45/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[5485])).
% 1.45/1.70 tff(5487,plain,
% 1.45/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.70 inference(transitivity,[status(thm)],[5486, 5484])).
% 1.45/1.70 tff(5488,plain,
% 1.45/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.45/1.70 inference(quant_inst,[status(thm)],[])).
% 1.45/1.70 tff(5489,plain,
% 1.45/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.45/1.70 inference(modus_ponens,[status(thm)],[5488, 5487])).
% 1.45/1.70 tff(5490,plain,
% 1.45/1.70 ($false),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[5489, 233, 5483, 284, 424, 5478])).
% 1.45/1.70 tff(5491,plain,((~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.70 tff(5492,plain,
% 1.45/1.70 (~r(z, s(s(z)))),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[5491, 247, 424, 284, 3244])).
% 1.45/1.70 tff(5493,plain,
% 1.45/1.70 (b(z, s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[357, 45, 5492, 352])).
% 1.55/1.70 tff(5494,plain,
% 1.55/1.70 (~b(z, s(s(s(z))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[2572, 5493, 284, 424])).
% 1.55/1.70 tff(5495,plain,
% 1.55/1.70 (r(z, s(s(s(z))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[78, 5494])).
% 1.55/1.70 tff(5496,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[2622, 108, 701, 2240, 5495, 247])).
% 1.55/1.70 tff(5497,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5498,plain,
% 1.55/1.70 (~r(s(s(s(z))), z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5497, 4304, 4305, 284, 5464, 3244])).
% 1.55/1.70 tff(5499,plain,
% 1.55/1.70 (b(s(s(s(z))), z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[244, 5498])).
% 1.55/1.70 tff(5500,plain,
% 1.55/1.70 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[2612, 97, 4305, 4304])).
% 1.55/1.70 tff(5501,plain,
% 1.55/1.70 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[186, 5500])).
% 1.55/1.70 tff(5502,plain,
% 1.55/1.70 (elem!1 = s(s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4578, 1677])).
% 1.55/1.70 tff(5503,plain,
% 1.55/1.70 (~b(elem!1, z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4394, 5502, 368])).
% 1.55/1.70 tff(5504,plain,
% 1.55/1.70 (r(elem!1, z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1037, 5503, 1046])).
% 1.55/1.70 tff(5505,plain,
% 1.55/1.70 (~r(elem!1, s(s(s(s(z)))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4366, 5504, 3244, 97])).
% 1.55/1.70 tff(5506,plain,
% 1.55/1.70 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.55/1.70 inference(monotonicity,[status(thm)],[1677])).
% 1.55/1.70 tff(5507,plain,
% 1.55/1.70 ((~r(s(s(s(s(z)))), s(s(z)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5506])).
% 1.55/1.70 tff(5508,plain,
% 1.55/1.70 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3354, 97, 3244, 4304])).
% 1.55/1.70 tff(5509,plain,
% 1.55/1.70 (~r(s(s(s(s(z)))), elem!1)),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5508, 5507])).
% 1.55/1.70 tff(5510,plain,
% 1.55/1.70 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[1677])).
% 1.55/1.70 tff(5511,plain,
% 1.55/1.70 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.55/1.70 inference(transitivity,[status(thm)],[5510, 808])).
% 1.55/1.70 tff(5512,plain,
% 1.55/1.70 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[5511, 852])).
% 1.55/1.70 tff(5513,plain,
% 1.55/1.70 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5512])).
% 1.55/1.70 tff(5514,plain,
% 1.55/1.70 (~(elem!1 = s(s(s(s(z)))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[169, 5513])).
% 1.55/1.70 tff(5515,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4601, 5514, 5509, 204, 707, 5505])).
% 1.55/1.70 tff(5516,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (elem!1 = z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5517,plain,
% 1.55/1.70 (~(s(s(z)) = elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5516, 707, 5501, 3244, 97, 1632, 368])).
% 1.55/1.70 tff(5518,plain,
% 1.55/1.70 (~r(s(s(s(z))), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4403, 97, 4305, 701])).
% 1.55/1.70 tff(5519,plain,
% 1.55/1.70 (b(elem!1, s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1236, 4383, 4727])).
% 1.55/1.70 tff(5520,plain,
% 1.55/1.70 (~b(s(s(s(z))), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4736, 920, 1009, 284])).
% 1.55/1.70 tff(5521,plain,
% 1.55/1.70 (s(s(s(z))) = elem!1),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[843, 5520, 4983])).
% 1.55/1.70 tff(5522,plain,
% 1.55/1.70 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5521])).
% 1.55/1.70 tff(5523,plain,
% 1.55/1.70 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.55/1.70 inference(symmetry,[status(thm)],[5522])).
% 1.55/1.70 tff(5524,plain,
% 1.55/1.70 (b(s(s(z)), s(s(s(z))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[920, 5523])).
% 1.55/1.70 tff(5525,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4303, 5524])).
% 1.55/1.70 tff(5526,plain,((~b(s(s(z)), elem!1)) | b(s(s(z)), s(s(s(z)))) | r(s(s(s(z))), elem!1) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5527,plain,
% 1.55/1.70 (~b(s(s(z)), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5526, 5519, 4303, 5518, 284])).
% 1.55/1.70 tff(5528,plain,
% 1.55/1.70 (r(s(s(z)), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1175, 5527, 1212])).
% 1.55/1.70 tff(5529,plain,
% 1.55/1.70 (~b(z, elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4355, 5519, 707, 272])).
% 1.55/1.70 tff(5530,plain,
% 1.55/1.70 (r(z, elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[934, 5529, 717])).
% 1.55/1.70 tff(5531,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4999, 5530, 5528, 1059, 701])).
% 1.55/1.70 tff(5532,plain,((~r(elem!1, z)) | (~r(s(s(z)), z)) | (z = elem!1) | (s(s(z)) = elem!1) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | b(s(s(z)), s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5533,plain,
% 1.55/1.70 (~r(elem!1, z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5532, 5517, 717, 4304, 707, 5499, 4303, 284, 97])).
% 1.55/1.70 tff(5534,plain,
% 1.55/1.70 (b(elem!1, z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1037, 5533, 1632])).
% 1.55/1.70 tff(5535,plain,
% 1.55/1.70 (~(elem!1 = s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1697, 5517])).
% 1.55/1.70 tff(5536,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5537,plain,
% 1.55/1.70 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5538,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5537])).
% 1.55/1.70 tff(5539,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[5538, 5536])).
% 1.55/1.70 tff(5540,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(5541,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5540, 5539])).
% 1.55/1.70 tff(5542,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5541, 233, 1009, 707, 284, 424])).
% 1.55/1.70 tff(5543,plain,((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5544,plain,
% 1.55/1.70 (~b(elem!1, s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5543, 707, 284, 5464])).
% 1.55/1.70 tff(5545,plain,
% 1.55/1.70 (r(elem!1, s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1236, 5544, 5535])).
% 1.55/1.70 tff(5546,plain,
% 1.55/1.70 (~(s(s(s(s(z)))) = elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[997, 5545, 5508])).
% 1.55/1.70 tff(5547,plain,
% 1.55/1.70 (~b(s(s(z)), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4503, 5534, 284, 707])).
% 1.55/1.70 tff(5548,plain,
% 1.55/1.70 (~r(s(s(s(s(z)))), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4520, 5544, 5535, 284, 5501, 5547])).
% 1.55/1.70 tff(5549,plain,
% 1.55/1.70 (b(s(s(s(s(z)))), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[860, 5548, 5546])).
% 1.55/1.70 tff(5550,plain,
% 1.55/1.70 (r(s(s(z)), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1175, 5547, 5517])).
% 1.55/1.70 tff(5551,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4481, 108, 938, 994, 701, 1213])).
% 1.55/1.70 tff(5552,plain,((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5553,plain,
% 1.55/1.70 (~r(z, elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5552, 5545, 4304, 5550])).
% 1.55/1.70 tff(5554,plain,
% 1.55/1.70 (b(z, elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[934, 5553, 717])).
% 1.55/1.70 tff(5555,plain,
% 1.55/1.70 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5556,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5555])).
% 1.55/1.70 tff(5557,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.55/1.70 inference(transitivity,[status(thm)],[5556, 1633])).
% 1.55/1.70 tff(5558,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(5559,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 1.55/1.70 tff(5560,plain,
% 1.55/1.70 (~b(s(s(s(s(z)))), z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5559, 233, 921, 809, 1071])).
% 1.55/1.70 tff(5561,plain,
% 1.55/1.70 (r(s(s(s(s(z)))), z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[629, 45, 89, 5560])).
% 1.55/1.70 tff(5562,plain,
% 1.55/1.70 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4531, 233, 809, 707, 1071])).
% 1.55/1.70 tff(5563,plain,
% 1.55/1.70 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[185, 45, 5562, 182])).
% 1.55/1.70 tff(5564,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5565,plain,
% 1.55/1.70 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5566,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5565])).
% 1.55/1.70 tff(5567,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.55/1.70 inference(transitivity,[status(thm)],[5566, 5564])).
% 1.55/1.70 tff(5568,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(5569,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5568, 5567])).
% 1.55/1.70 tff(5570,plain,
% 1.55/1.70 (~b(s(s(s(z))), z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5569, 233, 921, 809, 707])).
% 1.55/1.70 tff(5571,plain,
% 1.55/1.70 (r(s(s(s(z))), z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[243, 45, 65, 5570])).
% 1.55/1.70 tff(5572,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5573,plain,
% 1.55/1.70 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5574,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5573])).
% 1.55/1.70 tff(5575,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.55/1.70 inference(transitivity,[status(thm)],[5574, 5572])).
% 1.55/1.70 tff(5576,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(5577,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5576, 5575])).
% 1.55/1.70 tff(5578,plain,
% 1.55/1.70 (~b(z, s(s(s(z))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5577, 233, 921, 809, 707])).
% 1.55/1.70 tff(5579,plain,
% 1.55/1.70 (r(z, s(s(s(z))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[78, 5578])).
% 1.55/1.70 tff(5580,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3262, 108, 5579, 5571, 5563, 5561])).
% 1.55/1.70 tff(5581,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5582,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5581, 5554, 5549, 5534, 707])).
% 1.55/1.70 tff(5583,plain,((~b(s(s(s(z))), elem!1)) | (z = elem!1) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(z)), s(s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5584,plain,
% 1.55/1.70 (~b(s(s(s(z))), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5583, 79, 284, 4303, 717, 3244, 368])).
% 1.55/1.70 tff(5585,plain,
% 1.55/1.70 (s(s(s(z))) = elem!1),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[843, 5584, 4404])).
% 1.55/1.70 tff(5586,plain,
% 1.55/1.70 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5585])).
% 1.55/1.70 tff(5587,plain,
% 1.55/1.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.70 inference(symmetry,[status(thm)],[5586])).
% 1.55/1.70 tff(5588,plain,
% 1.55/1.70 (s(s(s(s(z)))) = s(elem!1)),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5585])).
% 1.55/1.70 tff(5589,plain,
% 1.55/1.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5588])).
% 1.55/1.70 tff(5590,plain,
% 1.55/1.70 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.55/1.70 inference(symmetry,[status(thm)],[5589])).
% 1.55/1.70 tff(5591,plain,
% 1.55/1.70 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[5590, 5587])).
% 1.55/1.70 tff(5592,plain,
% 1.55/1.70 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5591])).
% 1.55/1.70 tff(5593,plain,
% 1.55/1.70 (b(s(s(z)), s(elem!1))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[424, 4443])).
% 1.55/1.70 tff(5594,assumption,(~b(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.55/1.70 tff(5595,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5594, 5593])).
% 1.55/1.70 tff(5596,plain,(b(s(s(z)), s(elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5597,plain,
% 1.55/1.70 (b(s(s(z)), s(elem!1))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5596, 5585, 5464])).
% 1.55/1.70 tff(5598,plain,
% 1.55/1.70 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5588])).
% 1.55/1.70 tff(5599,plain,
% 1.55/1.70 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5585])).
% 1.55/1.70 tff(5600,plain,
% 1.55/1.70 (b(elem!1, s(s(s(s(z)))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5466, 5599])).
% 1.55/1.70 tff(5601,plain,
% 1.55/1.70 (b(elem!1, s(elem!1))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5600, 5598])).
% 1.55/1.70 tff(5602,plain,
% 1.55/1.70 (b(s(s(s(z))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5585])).
% 1.55/1.70 tff(5603,plain,
% 1.55/1.70 (b(elem!1, s(s(z)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[284, 5602])).
% 1.55/1.70 tff(5604,assumption,(b(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.55/1.70 tff(5605,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5606,plain,
% 1.55/1.70 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(5607,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5606])).
% 1.55/1.70 tff(5608,plain,
% 1.55/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.55/1.70 inference(transitivity,[status(thm)],[5607, 5605])).
% 1.55/1.70 tff(5609,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(5610,plain,
% 1.55/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5609, 5608])).
% 1.55/1.70 tff(5611,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5610, 233, 1009, 5368, 1289, 5604])).
% 1.55/1.70 tff(5612,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(5613,plain,
% 1.55/1.70 (~b(s(elem!1), elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5612, 5603, 5601, 5597])).
% 1.55/1.70 tff(5614,plain,
% 1.55/1.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[5613, 5592])).
% 1.55/1.70 tff(5615,plain,
% 1.55/1.70 (~b(s(z), s(s(s(s(z)))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4980, 5614, 79, 1632, 4305, 5499, 5468, 5466])).
% 1.55/1.70 tff(5616,plain,
% 1.55/1.70 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), elem!1)),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5585])).
% 1.55/1.70 tff(5617,plain,
% 1.55/1.70 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(z)), elem!1))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[5616])).
% 1.55/1.70 tff(5618,plain,
% 1.55/1.70 (~b(s(s(z)), elem!1)),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[4303, 5617])).
% 1.55/1.71 tff(5619,plain,
% 1.55/1.71 (~b(z, elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[4407, 5585, 54])).
% 1.55/1.71 tff(5620,plain,
% 1.55/1.71 (r(z, elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[934, 5619, 717])).
% 1.55/1.71 tff(5621,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.55/1.71 tff(5622,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5623,plain,
% 1.55/1.71 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5624,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5623])).
% 1.55/1.71 tff(5625,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[5624, 5622])).
% 1.55/1.71 tff(5626,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5627,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5626, 5625])).
% 1.55/1.71 tff(5628,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5627, 108, 701, 2240, 97, 5621])).
% 1.55/1.71 tff(5629,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(5630,plain,
% 1.55/1.71 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5629, 79, 4305, 4304])).
% 1.55/1.71 tff(5631,plain,
% 1.55/1.71 (s(s(s(z))) = elem!1),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[843, 797, 4983])).
% 1.55/1.71 tff(5632,plain,
% 1.55/1.71 (s(s(s(s(z)))) = s(elem!1)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5631])).
% 1.55/1.71 tff(5633,plain,
% 1.55/1.71 (s(elem!1) = s(s(s(s(z))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[5632])).
% 1.55/1.71 tff(5634,plain,
% 1.55/1.71 (elem!1 = s(s(s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[838, 5631])).
% 1.55/1.71 tff(5635,plain,
% 1.55/1.71 (~(elem!1 = s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1455, 5634])).
% 1.55/1.71 tff(5636,plain,
% 1.55/1.71 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5632])).
% 1.55/1.71 tff(5637,plain,
% 1.55/1.71 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5636])).
% 1.55/1.71 tff(5638,plain,
% 1.55/1.71 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[5637])).
% 1.55/1.71 tff(5639,plain,
% 1.55/1.71 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5638])).
% 1.55/1.71 tff(5640,plain,
% 1.55/1.71 (r(elem!1, s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[5639])).
% 1.55/1.71 tff(5641,plain,
% 1.55/1.71 ((~r(elem!1, s(s(s(s(s(s(z)))))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5640])).
% 1.55/1.71 tff(5642,plain,
% 1.55/1.71 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5631])).
% 1.55/1.71 tff(5643,plain,
% 1.55/1.71 ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) <=> (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5642])).
% 1.55/1.71 tff(5644,assumption,(~r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.55/1.71 tff(5645,plain,
% 1.55/1.71 (~r(elem!1, s(s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5644, 5643])).
% 1.55/1.71 tff(5646,plain,
% 1.55/1.71 (~r(elem!1, s(s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5645, 5641])).
% 1.55/1.71 tff(5647,plain,
% 1.55/1.71 (b(elem!1, s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1473, 5646, 5635])).
% 1.55/1.71 tff(5648,plain,
% 1.55/1.71 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5636])).
% 1.55/1.71 tff(5649,plain,
% 1.55/1.71 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5631])).
% 1.55/1.71 tff(5650,plain,
% 1.55/1.71 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.55/1.71 inference(transitivity,[status(thm)],[5649, 5648])).
% 1.55/1.71 tff(5651,plain,
% 1.55/1.71 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5631])).
% 1.55/1.71 tff(5652,plain,
% 1.55/1.71 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[5651])).
% 1.55/1.71 tff(5653,plain,
% 1.55/1.71 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[5636])).
% 1.55/1.71 tff(5654,plain,
% 1.55/1.71 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5653])).
% 1.55/1.71 tff(5655,plain,
% 1.55/1.71 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[5654, 5652])).
% 1.55/1.71 tff(5656,plain,
% 1.55/1.71 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5655])).
% 1.55/1.71 tff(5657,plain,
% 1.55/1.71 (r(s(z), s(elem!1))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1494, 5631, 52])).
% 1.55/1.71 tff(5658,plain,
% 1.55/1.71 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5632, 5636])).
% 1.55/1.71 tff(5659,plain,
% 1.55/1.71 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5633])).
% 1.55/1.71 tff(5660,plain,
% 1.55/1.71 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 1.55/1.71 inference(symmetry,[status(thm)],[5659])).
% 1.55/1.71 tff(5661,plain,
% 1.55/1.71 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5631])).
% 1.55/1.71 tff(5662,plain,
% 1.55/1.71 (b(elem!1, s(s(s(s(z)))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[204, 5661])).
% 1.55/1.71 tff(5663,plain,
% 1.55/1.71 (b(elem!1, s(elem!1))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5662, 5660])).
% 1.55/1.71 tff(5664,plain,
% 1.55/1.71 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[1254])).
% 1.55/1.71 tff(5665,plain,
% 1.55/1.71 ((~(s(s(s(s(s(z))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5664])).
% 1.55/1.71 tff(5666,plain,
% 1.55/1.71 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1270, 5634])).
% 1.55/1.71 tff(5667,plain,
% 1.55/1.71 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5666, 5665])).
% 1.55/1.71 tff(5668,plain,
% 1.55/1.71 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5653])).
% 1.55/1.71 tff(5669,plain,
% 1.55/1.71 ((~r(elem!1, s(s(elem!1)))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5668])).
% 1.55/1.71 tff(5670,plain,
% 1.55/1.71 (~(s(s(z)) = elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5434, 797, 284])).
% 1.55/1.71 tff(5671,plain,
% 1.55/1.71 (r(s(s(z)), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1175, 5670, 4424])).
% 1.55/1.71 tff(5672,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5673,plain,
% 1.55/1.71 (((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5674,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5673])).
% 1.55/1.71 tff(5675,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[5674, 5672])).
% 1.55/1.71 tff(5676,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5677,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5676, 5675])).
% 1.55/1.71 tff(5678,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5677, 108, 938, 701, 1213, 1387])).
% 1.55/1.71 tff(5679,plain,((~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(5680,plain,
% 1.55/1.71 (~r(elem!1, s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5679, 5671, 701, 938])).
% 1.55/1.71 tff(5681,plain,
% 1.55/1.71 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5680, 5669])).
% 1.55/1.71 tff(5682,plain,
% 1.55/1.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5683,plain,
% 1.55/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5684,plain,
% 1.55/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5683, 5682])).
% 1.55/1.71 tff(5685,plain,
% 1.55/1.71 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5684, 45])).
% 1.55/1.71 tff(5686,plain,
% 1.55/1.71 (b(elem!1, s(s(s(s(s(z))))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5685, 5681, 5667])).
% 1.55/1.71 tff(5687,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.55/1.71 tff(5688,plain,
% 1.55/1.71 (b(elem!1, s(s(elem!1)))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5687, 5205])).
% 1.55/1.71 tff(5689,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1302, 5688])).
% 1.55/1.71 tff(5690,plain,((~b(elem!1, s(s(s(s(s(z))))))) | b(elem!1, s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(5691,plain,
% 1.55/1.71 (b(elem!1, s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5690, 5686, 5631])).
% 1.55/1.71 tff(5692,plain,
% 1.55/1.71 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5653, 5632])).
% 1.55/1.71 tff(5693,plain,
% 1.55/1.71 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[5692])).
% 1.55/1.71 tff(5694,plain,
% 1.55/1.71 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5693])).
% 1.55/1.71 tff(5695,plain,
% 1.55/1.71 (~(elem!1 = s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[4817, 5634])).
% 1.55/1.71 tff(5696,plain,
% 1.55/1.71 (~(s(s(s(s(z)))) = elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[855, 5695])).
% 1.55/1.71 tff(5697,plain,
% 1.55/1.71 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1245, 5696])).
% 1.55/1.71 tff(5698,plain,
% 1.55/1.71 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5697, 5694])).
% 1.55/1.71 tff(5699,plain,
% 1.55/1.71 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5633])).
% 1.55/1.71 tff(5700,plain,
% 1.55/1.71 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.55/1.71 inference(symmetry,[status(thm)],[5699])).
% 1.55/1.71 tff(5701,plain,
% 1.55/1.71 (r(s(s(s(s(z)))), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[4833, 797, 3244, 4306, 97])).
% 1.55/1.71 tff(5702,plain,
% 1.55/1.71 (r(s(elem!1), elem!1)),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5701, 5700])).
% 1.55/1.71 tff(5703,plain,
% 1.55/1.71 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5631])).
% 1.55/1.71 tff(5704,plain,
% 1.55/1.71 (b(elem!1, s(z))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[1072, 5703])).
% 1.55/1.71 tff(5705,plain,
% 1.55/1.71 ((~r(s(s(elem!1)), s(z))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5387])).
% 1.55/1.71 tff(5706,plain,
% 1.55/1.71 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1245, 4819])).
% 1.55/1.71 tff(5707,plain,
% 1.55/1.71 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5706, 1383])).
% 1.55/1.71 tff(5708,plain,
% 1.55/1.71 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1409, 5233, 5707])).
% 1.55/1.71 tff(5709,plain,
% 1.55/1.71 (r(s(s(elem!1)), s(elem!1))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5708, 5221])).
% 1.55/1.71 tff(5710,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5711,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5712,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5711, 5710])).
% 1.55/1.71 tff(5713,plain,
% 1.55/1.71 ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5712, 108, 5153, 1497])).
% 1.55/1.71 tff(5714,plain,
% 1.55/1.71 (~r(s(s(elem!1)), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5713, 5709])).
% 1.55/1.71 tff(5715,plain,
% 1.55/1.71 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5714, 5705])).
% 1.55/1.71 tff(5716,plain,
% 1.55/1.71 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[556, 5715, 5188])).
% 1.55/1.71 tff(5717,plain,
% 1.55/1.71 (b(s(s(elem!1)), s(z))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5716, 1279])).
% 1.55/1.71 tff(5718,plain,
% 1.55/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5719,plain,
% 1.55/1.71 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5720,plain,
% 1.55/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5719])).
% 1.55/1.71 tff(5721,plain,
% 1.55/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[5720, 5718])).
% 1.55/1.71 tff(5722,plain,
% 1.55/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5723,plain,
% 1.55/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5722, 5721])).
% 1.55/1.71 tff(5724,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5723, 233, 1290, 967, 1328, 5717])).
% 1.55/1.71 tff(5725,plain,((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~(s(s(s(z))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(5726,plain,
% 1.55/1.71 (~b(s(z), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5725, 5691, 5704, 5631, 5702, 5657])).
% 1.55/1.71 tff(5727,plain,
% 1.55/1.71 (r(s(z), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1352, 5726])).
% 1.55/1.71 tff(5728,plain,
% 1.55/1.71 (r(s(s(elem!1)), s(elem!1))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[1400, 5221])).
% 1.55/1.71 tff(5729,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5730,plain,
% 1.55/1.71 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5731,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5730])).
% 1.55/1.71 tff(5732,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[5731, 5729])).
% 1.55/1.71 tff(5733,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5734,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5733, 5732])).
% 1.55/1.71 tff(5735,plain,
% 1.55/1.71 (~r(s(s(elem!1)), s(elem!1))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5734, 108, 5153, 1388, 1497])).
% 1.55/1.71 tff(5736,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5735, 5728])).
% 1.55/1.71 tff(5737,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(5738,plain,
% 1.55/1.71 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5737, 5727, 5702, 5631, 5657])).
% 1.55/1.71 tff(5739,plain,
% 1.55/1.71 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1409, 5738, 5698])).
% 1.55/1.71 tff(5740,plain,
% 1.55/1.71 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1417, 5739, 5631])).
% 1.55/1.71 tff(5741,plain,
% 1.55/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5742,plain,
% 1.55/1.71 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5743,plain,
% 1.55/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5742])).
% 1.55/1.71 tff(5744,plain,
% 1.55/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[5743, 5741])).
% 1.55/1.71 tff(5745,plain,
% 1.55/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5746,plain,
% 1.55/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5745, 5744])).
% 1.55/1.71 tff(5747,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5746, 233, 5368, 1290, 1287, 5223])).
% 1.55/1.71 tff(5748,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(5749,plain,
% 1.55/1.71 (~b(s(elem!1), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5748, 5740, 5691, 5663])).
% 1.55/1.71 tff(5750,plain,
% 1.55/1.71 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1277, 5749, 5631])).
% 1.55/1.71 tff(5751,plain,
% 1.55/1.71 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[745, 5750])).
% 1.55/1.71 tff(5752,plain,
% 1.55/1.71 (r(s(elem!1), s(s(elem!1)))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[5751, 5658])).
% 1.55/1.71 tff(5753,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5754,plain,
% 1.55/1.71 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(5755,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[5754])).
% 1.55/1.71 tff(5756,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[5755, 5753])).
% 1.55/1.71 tff(5757,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(5758,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5757, 5756])).
% 1.55/1.72 tff(5759,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5758, 108, 1388, 4656, 5386, 1497])).
% 1.55/1.72 tff(5760,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5761,plain,
% 1.55/1.72 (~r(s(s(elem!1)), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5760, 5727, 5752, 5657])).
% 1.55/1.72 tff(5762,plain,
% 1.55/1.72 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5761, 5656])).
% 1.55/1.72 tff(5763,plain,
% 1.55/1.72 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[598, 5762])).
% 1.55/1.72 tff(5764,plain,
% 1.55/1.72 (b(s(s(elem!1)), elem!1)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5763, 5650])).
% 1.55/1.72 tff(5765,plain,
% 1.55/1.72 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1376, 5631])).
% 1.55/1.72 tff(5766,plain,
% 1.55/1.72 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5636])).
% 1.55/1.72 tff(5767,plain,
% 1.55/1.72 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5636])).
% 1.55/1.72 tff(5768,plain,
% 1.55/1.72 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.55/1.72 inference(transitivity,[status(thm)],[5767, 4684])).
% 1.55/1.72 tff(5769,plain,
% 1.55/1.72 ((s(z) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.55/1.72 inference(symmetry,[status(thm)],[5768])).
% 1.55/1.72 tff(5770,plain,
% 1.55/1.72 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(z)))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5769])).
% 1.55/1.72 tff(5771,plain,
% 1.55/1.72 (~(s(s(s(s(s(z))))) = s(z))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[1348, 5770])).
% 1.55/1.72 tff(5772,plain,
% 1.55/1.72 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5398, 5631, 5727, 5752, 5657])).
% 1.55/1.72 tff(5773,plain,
% 1.55/1.72 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[556, 5772, 5771])).
% 1.55/1.72 tff(5774,plain,
% 1.55/1.72 (b(s(s(elem!1)), s(z))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5773, 5766])).
% 1.55/1.72 tff(5775,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.55/1.72 tff(5776,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5777,plain,
% 1.55/1.72 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5778,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5777])).
% 1.55/1.72 tff(5779,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[5778, 5776])).
% 1.55/1.72 tff(5780,plain,
% 1.55/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(5781,plain,
% 1.55/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5780, 5779])).
% 1.55/1.72 tff(5782,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5781, 233, 967, 1288, 5775, 1419])).
% 1.55/1.72 tff(5783,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5784,plain,
% 1.55/1.72 (~b(s(z), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5783, 5704, 5774, 5764])).
% 1.55/1.72 tff(5785,plain,
% 1.55/1.72 (r(s(z), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1441, 5784])).
% 1.55/1.72 tff(5786,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5787,plain,
% 1.55/1.72 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5788,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5787])).
% 1.55/1.72 tff(5789,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[5788, 5786])).
% 1.55/1.72 tff(5790,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(5791,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5790, 5789])).
% 1.55/1.72 tff(5792,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5791, 108, 5153, 1576, 1575, 1497])).
% 1.55/1.72 tff(5793,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5794,plain,
% 1.55/1.72 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5793, 5785, 5702, 5657])).
% 1.55/1.72 tff(5795,plain,
% 1.55/1.72 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1593, 5794, 5631])).
% 1.55/1.72 tff(5796,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1598, 5795, 5765])).
% 1.55/1.72 tff(5797,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1605, 5796, 5631])).
% 1.55/1.72 tff(5798,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5799,plain,
% 1.55/1.72 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5800,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5799])).
% 1.55/1.72 tff(5801,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.55/1.72 inference(transitivity,[status(thm)],[5800, 5798])).
% 1.55/1.72 tff(5802,plain,
% 1.55/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(5803,plain,
% 1.55/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5802, 5801])).
% 1.55/1.72 tff(5804,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5803, 233, 1460, 5775, 1786, 5272])).
% 1.55/1.72 tff(5805,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5806,plain,
% 1.55/1.72 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5805, 5797, 5764, 5647])).
% 1.55/1.72 tff(5807,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5808,plain,
% 1.55/1.72 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5809,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5808])).
% 1.55/1.72 tff(5810,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[5809, 5807])).
% 1.55/1.72 tff(5811,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(5812,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5811, 5810])).
% 1.55/1.72 tff(5813,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5812, 108, 5238, 1388, 5386, 1497])).
% 1.55/1.72 tff(5814,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5815,plain,
% 1.55/1.72 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5814, 5727, 5752, 5657])).
% 1.55/1.72 tff(5816,plain,
% 1.55/1.72 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1616, 45, 5815])).
% 1.55/1.72 tff(5817,plain,
% 1.55/1.72 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5816, 5806])).
% 1.55/1.72 tff(5818,plain,
% 1.55/1.72 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5817])).
% 1.55/1.72 tff(5819,plain,
% 1.55/1.72 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.55/1.72 inference(symmetry,[status(thm)],[5818])).
% 1.55/1.72 tff(5820,plain,
% 1.55/1.72 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.55/1.72 inference(symmetry,[status(thm)],[5817])).
% 1.55/1.72 tff(5821,plain,
% 1.55/1.72 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[5820, 1368, 5819, 1342, 5633])).
% 1.55/1.72 tff(5822,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5765, 5821])).
% 1.55/1.72 tff(5823,plain,(b(s(s(s(z))), elem!1) | (~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(z)), elem!1) | r(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(s(z)))), s(s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5824,plain,
% 1.55/1.72 (~r(s(z), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5823, 5614, 5584, 4304, 5630, 5468, 5466, 5620, 4404, 284, 3244, 5618, 79])).
% 1.55/1.72 tff(5825,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1122, 5824, 5615])).
% 1.55/1.72 tff(5826,plain,(b(z, s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z)))) | (z = elem!1) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5827,plain,
% 1.55/1.72 (b(z, s(s(s(z))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5826, 368, 3244, 4303, 717, 284])).
% 1.55/1.72 tff(5828,plain,
% 1.55/1.72 (~b(z, s(s(z)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2572, 5827, 284, 5464])).
% 1.55/1.72 tff(5829,plain,
% 1.55/1.72 (r(z, s(s(z)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[359, 5828])).
% 1.55/1.72 tff(5830,plain,
% 1.55/1.72 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3276, 5829, 3244, 4305])).
% 1.55/1.72 tff(5831,plain,
% 1.55/1.72 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[462, 5830])).
% 1.55/1.72 tff(5832,plain,
% 1.55/1.72 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3364, 5831, 284, 5464])).
% 1.55/1.72 tff(5833,plain,
% 1.55/1.72 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[186, 5832])).
% 1.55/1.72 tff(5834,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5835,plain,
% 1.55/1.72 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5836,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5835])).
% 1.55/1.72 tff(5837,plain,
% 1.55/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[5836, 5834])).
% 1.55/1.72 tff(5838,plain,
% 1.55/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(5839,plain,
% 1.55/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5838, 5837])).
% 1.55/1.72 tff(5840,plain,
% 1.55/1.72 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5839, 233, 284, 5831, 5464])).
% 1.55/1.72 tff(5841,plain,
% 1.55/1.72 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[386, 5840])).
% 1.55/1.72 tff(5842,plain,
% 1.55/1.72 (~b(s(z), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[291, 233, 284, 273, 1989])).
% 1.55/1.72 tff(5843,plain,
% 1.55/1.72 (r(s(z), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[260, 5842])).
% 1.55/1.72 tff(5844,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5845,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(5846,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[5845, 5844])).
% 1.55/1.72 tff(5847,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5846, 108, 493, 3244, 52, 5843])).
% 1.55/1.72 tff(5848,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(5849,plain,
% 1.55/1.72 (~r(s(z), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5848, 5829, 3244, 284, 5827, 5841, 5833])).
% 1.55/1.72 tff(5850,plain,
% 1.55/1.72 (b(s(z), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1122, 5849])).
% 1.55/1.72 tff(5851,plain,
% 1.55/1.72 (~b(s(z), s(s(z)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3205, 233, 5831, 5464, 5850])).
% 1.55/1.72 tff(5852,plain,
% 1.55/1.72 (r(s(z), s(s(z)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[481, 45, 34, 5851])).
% 1.55/1.72 tff(5853,plain,
% 1.55/1.72 (~b(s(s(z)), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3213, 233, 5831, 5464, 5850])).
% 1.55/1.72 tff(5854,plain,
% 1.55/1.72 (r(s(s(z)), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[48, 45, 35, 5853])).
% 1.55/1.72 tff(5855,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5856,plain,
% 1.55/1.72 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(5857,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[5856])).
% 1.55/1.72 tff(5858,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.55/1.73 inference(transitivity,[status(thm)],[5857, 5855])).
% 1.55/1.73 tff(5859,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(5860,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[5859, 5858])).
% 1.55/1.73 tff(5861,plain,
% 1.55/1.73 (~r(s(z), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5860, 108, 5829, 4305, 5852])).
% 1.55/1.73 tff(5862,plain,
% 1.55/1.73 (b(s(z), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[260, 5861])).
% 1.55/1.73 tff(5863,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5864,plain,
% 1.55/1.73 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5865,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[5864])).
% 1.55/1.73 tff(5866,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.55/1.73 inference(transitivity,[status(thm)],[5865, 5863])).
% 1.55/1.73 tff(5867,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(5868,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[5867, 5866])).
% 1.55/1.73 tff(5869,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5868, 233, 5827, 5499, 5862])).
% 1.55/1.73 tff(5870,plain,
% 1.55/1.73 (r(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1090, 5869])).
% 1.55/1.73 tff(5871,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3535, 108, 4305, 5870, 5854, 5852])).
% 1.55/1.73 tff(5872,plain,(b(s(s(z)), z) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z)))) | b(s(s(z)), s(s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5873,plain,
% 1.55/1.73 (b(s(s(z)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5872, 4303, 284, 3244, 717])).
% 1.55/1.73 tff(5874,plain,
% 1.55/1.73 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3276, 493, 3244, 2240])).
% 1.55/1.73 tff(5875,plain,
% 1.55/1.73 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[462, 5874])).
% 1.55/1.73 tff(5876,plain,
% 1.55/1.73 (~r(z, s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3326, 649, 284, 3244, 2240])).
% 1.55/1.73 tff(5877,plain,
% 1.55/1.73 (b(z, s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[78, 5876])).
% 1.55/1.73 tff(5878,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5879,plain,
% 1.55/1.73 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5880,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[5879])).
% 1.55/1.73 tff(5881,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.55/1.73 inference(transitivity,[status(thm)],[5880, 5878])).
% 1.55/1.73 tff(5882,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(5883,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[5882, 5881])).
% 1.55/1.73 tff(5884,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5883, 233, 284, 273, 649, 272])).
% 1.55/1.73 tff(5885,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5886,plain,
% 1.55/1.73 (~b(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5885, 5877, 284, 649])).
% 1.55/1.73 tff(5887,plain,
% 1.55/1.73 (r(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[244, 5886])).
% 1.55/1.73 tff(5888,plain,
% 1.55/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5476, 493, 3244, 5887])).
% 1.55/1.73 tff(5889,plain,
% 1.55/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[186, 5888])).
% 1.55/1.73 tff(5890,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2398, 5889, 5875, 284, 649])).
% 1.55/1.73 tff(5891,plain,((~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5892,plain,
% 1.55/1.73 (~r(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5891, 5873, 284, 3244, 4305])).
% 1.55/1.73 tff(5893,plain,
% 1.55/1.73 (b(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[359, 5892])).
% 1.55/1.73 tff(5894,plain,
% 1.55/1.73 (~r(z, s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3326, 5873, 284, 3244, 4305])).
% 1.55/1.73 tff(5895,plain,
% 1.55/1.73 (b(z, s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[78, 5894])).
% 1.55/1.73 tff(5896,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5897,plain,
% 1.55/1.73 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5898,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[5897])).
% 1.55/1.73 tff(5899,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[5898, 5896])).
% 1.55/1.73 tff(5900,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(5901,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[5900, 5899])).
% 1.55/1.73 tff(5902,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5901, 233, 284, 5895, 5893, 5873])).
% 1.55/1.73 tff(5903,plain,(b(s(s(z)), s(s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5904,plain,
% 1.55/1.73 (z = elem!1),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5903, 4302, 4075, 4082])).
% 1.55/1.73 tff(5905,plain,
% 1.55/1.73 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.55/1.73 inference(monotonicity,[status(thm)],[5904])).
% 1.55/1.73 tff(5906,plain,
% 1.55/1.73 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = z)),
% 1.55/1.73 inference(symmetry,[status(thm)],[5905])).
% 1.55/1.73 tff(5907,plain,
% 1.55/1.73 (~b(s(s(z)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3326, 4302, 79, 4076, 4082])).
% 1.55/1.73 tff(5908,plain,
% 1.55/1.73 (r(s(s(z)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[374, 5907])).
% 1.55/1.73 tff(5909,plain,
% 1.55/1.73 (~r(s(s(s(z))), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4403, 5908, 79, 4076])).
% 1.55/1.73 tff(5910,plain,
% 1.55/1.73 (elem!1 = z),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1056, 5904])).
% 1.55/1.73 tff(5911,plain,
% 1.55/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2612, 5908, 79, 4076])).
% 1.55/1.73 tff(5912,plain,
% 1.55/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[186, 5911])).
% 1.55/1.73 tff(5913,plain,
% 1.55/1.73 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3354, 5908, 79, 4082])).
% 1.55/1.73 tff(5914,plain,
% 1.55/1.73 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[462, 5913])).
% 1.55/1.73 tff(5915,plain,
% 1.55/1.73 (~b(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4010, 5914, 4082, 4302, 5912])).
% 1.55/1.73 tff(5916,plain,
% 1.55/1.73 (~b(s(s(s(z))), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3707, 5915, 5910])).
% 1.55/1.73 tff(5917,plain,
% 1.55/1.73 (s(s(s(z))) = elem!1),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[843, 5916, 5909])).
% 1.55/1.73 tff(5918,plain,
% 1.55/1.73 (s(s(s(z))) = z),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[5917, 5906])).
% 1.55/1.73 tff(5919,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[65, 5918])).
% 1.55/1.73 tff(5920,plain,(b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5921,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[281, 272, 5920, 53])).
% 1.55/1.73 tff(5922,plain,
% 1.55/1.73 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[186, 5921])).
% 1.55/1.73 tff(5923,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2691, 272, 5920, 53])).
% 1.55/1.73 tff(5924,plain,
% 1.55/1.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[386, 5923])).
% 1.55/1.73 tff(5925,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3537, 5924, 5922, 53])).
% 1.55/1.73 tff(5926,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5927,plain,
% 1.55/1.73 (~b(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5926, 53])).
% 1.55/1.73 tff(5928,plain,
% 1.55/1.73 (r(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[244, 5927])).
% 1.55/1.73 tff(5929,plain,
% 1.55/1.73 (~b(s(z), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3113, 53, 5920])).
% 1.55/1.73 tff(5930,plain,
% 1.55/1.73 (r(s(z), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[260, 5929])).
% 1.55/1.73 tff(5931,plain,
% 1.55/1.73 (~b(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3121, 233, 284, 80, 5920])).
% 1.55/1.73 tff(5932,plain,
% 1.55/1.73 (r(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[359, 5931])).
% 1.55/1.73 tff(5933,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5934,plain,
% 1.55/1.73 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5935,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[5934])).
% 1.55/1.73 tff(5936,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[5935, 5933])).
% 1.55/1.73 tff(5937,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(5938,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[5937, 5936])).
% 1.55/1.73 tff(5939,plain,
% 1.55/1.73 (~r(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5938, 108, 5932, 247, 246])).
% 1.55/1.73 tff(5940,plain,
% 1.55/1.73 (b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1090, 5939])).
% 1.55/1.73 tff(5941,plain,
% 1.55/1.73 (~b(s(s(z)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3129, 233, 284, 80, 5920])).
% 1.55/1.73 tff(5942,plain,
% 1.55/1.73 (r(s(s(z)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[374, 5941])).
% 1.55/1.73 tff(5943,plain,
% 1.55/1.73 (~r(s(s(z)), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2963, 108, 5942, 5932, 246])).
% 1.55/1.73 tff(5944,plain,
% 1.55/1.73 (b(s(s(z)), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[50, 5943])).
% 1.55/1.73 tff(5945,plain,
% 1.55/1.73 (~r(s(z), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2971, 108, 5942, 5932, 246])).
% 1.55/1.73 tff(5946,plain,
% 1.55/1.73 (b(s(z), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2414, 5945])).
% 1.55/1.73 tff(5947,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2986, 5946, 5944, 80, 5940])).
% 1.55/1.73 tff(5948,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5949,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5948, 80, 5930, 5928])).
% 1.55/1.73 tff(5950,plain,
% 1.55/1.73 (r(s(s(s(z))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[340, 5949])).
% 1.55/1.73 tff(5951,plain,
% 1.55/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2953, 5950, 5920, 53, 5928, 80])).
% 1.55/1.73 tff(5952,plain,
% 1.55/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[186, 5951])).
% 1.55/1.73 tff(5953,plain,
% 1.55/1.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[432, 5952, 53, 80])).
% 1.55/1.73 tff(5954,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[617, 5952, 5920, 53])).
% 1.55/1.73 tff(5955,plain,
% 1.55/1.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[386, 5954])).
% 1.55/1.73 tff(5956,plain,
% 1.55/1.73 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1928, 5955, 5950, 5953])).
% 1.55/1.73 tff(5957,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3241, 5952, 53, 2751])).
% 1.55/1.73 tff(5958,plain,
% 1.55/1.73 (r(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1090, 5957])).
% 1.55/1.73 tff(5959,plain,
% 1.55/1.73 (~r(z, s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[986, 5958, 5930, 5928])).
% 1.55/1.73 tff(5960,plain,
% 1.55/1.73 (b(z, s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[222, 5959])).
% 1.55/1.73 tff(5961,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5962,plain,
% 1.55/1.73 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(5963,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[5962])).
% 1.55/1.73 tff(5964,plain,
% 1.55/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[5963, 5961])).
% 1.55/1.73 tff(5965,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(5966,plain,
% 1.55/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 1.55/1.73 tff(5967,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5966, 233, 273, 442, 1930, 204])).
% 1.55/1.73 tff(5968,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5969,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5968, 5960, 5956, 5920, 5952])).
% 1.55/1.73 tff(5970,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5971,plain,
% 1.55/1.73 (~b(s(s(z)), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5970, 53])).
% 1.55/1.73 tff(5972,plain,
% 1.55/1.73 (r(s(s(z)), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2228, 5971])).
% 1.55/1.73 tff(5973,plain,
% 1.55/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3587, 5972, 53])).
% 1.55/1.73 tff(5974,plain,
% 1.55/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[186, 5973])).
% 1.55/1.73 tff(5975,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[617, 5974, 5920, 53])).
% 1.55/1.73 tff(5976,plain,
% 1.55/1.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[386, 5975])).
% 1.55/1.73 tff(5977,plain,
% 1.55/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3587, 2240, 53])).
% 1.55/1.73 tff(5978,plain,
% 1.55/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[186, 5977])).
% 1.55/1.73 tff(5979,plain,
% 1.55/1.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2658, 5978, 53, 284])).
% 1.55/1.73 tff(5980,plain,
% 1.55/1.73 (r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[440, 5979])).
% 1.55/1.73 tff(5981,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3241, 5978, 53, 2751])).
% 1.55/1.73 tff(5982,plain,
% 1.55/1.73 (r(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1090, 5981])).
% 1.55/1.73 tff(5983,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[617, 5978, 5920, 53])).
% 1.55/1.73 tff(5984,plain,
% 1.55/1.73 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[386, 5983])).
% 1.55/1.73 tff(5985,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4326, 5984, 5982, 2240, 5980])).
% 1.55/1.73 tff(5986,plain,((~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5987,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5986, 5972, 53])).
% 1.55/1.73 tff(5988,plain,
% 1.55/1.73 (r(s(s(s(z))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[340, 5987])).
% 1.55/1.73 tff(5989,plain,
% 1.55/1.73 (~b(s(s(z)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2237, 5988, 5920, 53])).
% 1.55/1.73 tff(5990,plain,
% 1.55/1.73 (r(s(s(z)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[374, 5989])).
% 1.55/1.73 tff(5991,plain,
% 1.55/1.73 (~b(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2520, 5990, 53, 5972, 5988, 5976])).
% 1.55/1.73 tff(5992,plain,
% 1.55/1.73 (~r(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[703, 5990, 5928, 5988])).
% 1.55/1.73 tff(5993,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[359, 5992, 5991])).
% 1.55/1.73 tff(5994,plain,(~b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(5995,plain,
% 1.55/1.73 (r(s(s(s(s(z)))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3228, 5994])).
% 1.55/1.73 tff(5996,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.55/1.73 tff(5997,plain,
% 1.55/1.73 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[186, 5996])).
% 1.55/1.73 tff(5998,plain,
% 1.55/1.73 (~r(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5476, 247, 5995, 81])).
% 1.55/1.73 tff(5999,plain,
% 1.55/1.73 (b(z, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[359, 5998])).
% 1.55/1.73 tff(6000,plain,
% 1.55/1.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2572, 5999, 5920, 284])).
% 1.55/1.73 tff(6001,plain,
% 1.55/1.73 (r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[440, 6000])).
% 1.55/1.73 tff(6002,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(6003,plain,
% 1.55/1.73 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(6004,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[6003])).
% 1.55/1.73 tff(6005,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.55/1.73 inference(transitivity,[status(thm)],[6004, 6002])).
% 1.55/1.73 tff(6006,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(6007,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[6006, 6005])).
% 1.55/1.73 tff(6008,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[6007, 108, 247, 81, 978, 3244])).
% 1.55/1.73 tff(6009,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(6010,plain,
% 1.55/1.73 (~r(z, s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[6009, 247, 5995, 81])).
% 1.55/1.73 tff(6011,plain,
% 1.55/1.73 (b(z, s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[222, 6010])).
% 1.55/1.74 tff(6012,plain,
% 1.55/1.74 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[5448, 6011, 5920, 284])).
% 1.55/1.74 tff(6013,plain,
% 1.55/1.74 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[386, 6012])).
% 1.55/1.74 tff(6014,plain,
% 1.55/1.74 (~r(s(s(z)), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2598, 6013, 81, 6001])).
% 1.55/1.74 tff(6015,plain,
% 1.55/1.74 (b(s(s(z)), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2228, 6014])).
% 1.55/1.74 tff(6016,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[3121, 233, 284, 6015, 5920, 5999])).
% 1.55/1.74 tff(6017,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(6018,plain,
% 1.55/1.74 (~r(s(s(s(z))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6017, 284, 5997])).
% 1.55/1.74 tff(6019,plain,
% 1.55/1.74 (b(s(s(s(z))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[244, 6018])).
% 1.55/1.74 tff(6020,plain,
% 1.55/1.74 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.55/1.74 inference(commutativity,[status(thm)],[])).
% 1.55/1.74 tff(6021,plain,
% 1.55/1.74 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.55/1.74 inference(symmetry,[status(thm)],[6020])).
% 1.55/1.74 tff(6022,plain,
% 1.55/1.74 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[6021])).
% 1.55/1.74 tff(6023,plain,
% 1.55/1.74 (~(s(z) = s(s(s(s(s(z))))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[91, 6022])).
% 1.55/1.74 tff(6024,plain,
% 1.55/1.74 (~r(s(s(s(z))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6017, 284, 81])).
% 1.55/1.74 tff(6025,plain,
% 1.55/1.74 (b(s(s(s(z))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[244, 6024])).
% 1.55/1.74 tff(6026,plain,
% 1.55/1.74 (~b(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2069, 80, 6025, 284])).
% 1.55/1.74 tff(6027,plain,
% 1.55/1.74 (r(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[359, 6026])).
% 1.55/1.74 tff(6028,plain,
% 1.55/1.74 (~r(s(z), s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[5848, 6027, 5920, 5995, 284, 130, 81])).
% 1.55/1.74 tff(6029,plain,
% 1.55/1.74 (b(s(z), s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1122, 6028])).
% 1.55/1.74 tff(6030,plain,
% 1.55/1.74 (~b(s(s(z)), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[5885, 6025, 5920, 284])).
% 1.55/1.74 tff(6031,plain,
% 1.55/1.74 (r(s(s(z)), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[374, 6030])).
% 1.55/1.74 tff(6032,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6033,plain,
% 1.55/1.74 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6034,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[6033])).
% 1.55/1.74 tff(6035,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[6034, 6032])).
% 1.55/1.74 tff(6036,plain,
% 1.55/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(6037,plain,
% 1.55/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[6036, 6035])).
% 1.55/1.74 tff(6038,plain,
% 1.55/1.74 (~b(s(s(s(s(s(z))))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6037, 233, 284, 5920, 1547])).
% 1.55/1.74 tff(6039,plain,
% 1.55/1.74 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[517, 45, 514, 6038])).
% 1.55/1.74 tff(6040,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6041,plain,
% 1.55/1.74 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6042,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[6041])).
% 1.55/1.74 tff(6043,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[6042, 6040])).
% 1.55/1.74 tff(6044,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(6045,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[6044, 6043])).
% 1.55/1.74 tff(6046,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6045, 108, 701, 493, 6039, 3603])).
% 1.55/1.74 tff(6047,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(6048,plain,
% 1.55/1.74 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6047, 6027, 6031, 284, 80])).
% 1.55/1.74 tff(6049,plain,
% 1.55/1.74 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[598, 6048])).
% 1.55/1.74 tff(6050,plain,
% 1.55/1.74 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2735, 108, 130, 81, 6049])).
% 1.55/1.74 tff(6051,plain,
% 1.55/1.74 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[579, 45, 576, 6050])).
% 1.55/1.74 tff(6052,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6053,plain,
% 1.55/1.74 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6054,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[6053])).
% 1.55/1.74 tff(6055,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[6054, 6052])).
% 1.55/1.74 tff(6056,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(6057,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[6056, 6055])).
% 1.55/1.74 tff(6058,plain,
% 1.55/1.74 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6057, 108, 130, 81, 6049])).
% 1.55/1.74 tff(6059,plain,
% 1.55/1.74 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[745, 6058])).
% 1.55/1.74 tff(6060,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6061,plain,
% 1.55/1.74 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6062,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[6061])).
% 1.55/1.74 tff(6063,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[6062, 6060])).
% 1.55/1.74 tff(6064,plain,
% 1.55/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(6065,plain,
% 1.55/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[6064, 6063])).
% 1.55/1.74 tff(6066,plain,
% 1.55/1.74 (~b(s(z), s(s(s(s(s(z))))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6065, 233, 6059, 6051, 6029])).
% 1.55/1.74 tff(6067,plain,
% 1.55/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6068,plain,
% 1.55/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(6069,plain,
% 1.55/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[6068, 6067])).
% 1.55/1.74 tff(6070,plain,
% 1.55/1.74 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6069, 45, 6066])).
% 1.55/1.74 tff(6071,plain,
% 1.55/1.74 (r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6070, 6023])).
% 1.55/1.74 tff(6072,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6073,plain,
% 1.55/1.74 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6074,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[6073])).
% 1.55/1.74 tff(6075,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[6074, 6072])).
% 1.55/1.74 tff(6076,plain,
% 1.55/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(6077,plain,
% 1.55/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[6076, 6075])).
% 1.55/1.74 tff(6078,plain,
% 1.55/1.74 (~b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6077, 233, 6059, 6051, 6029])).
% 1.55/1.74 tff(6079,plain,
% 1.55/1.74 (r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[3933, 6078])).
% 1.55/1.74 tff(6080,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.55/1.74 tff(6081,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6082,plain,
% 1.55/1.74 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6083,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[6082])).
% 1.55/1.74 tff(6084,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[6083, 6081])).
% 1.55/1.74 tff(6085,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(6086,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[6085, 6084])).
% 1.55/1.74 tff(6087,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6086, 108, 92, 1537, 747, 6080])).
% 1.55/1.74 tff(6088,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(6089,plain,
% 1.55/1.74 (~r(s(s(s(z))), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6088, 6049, 6079, 6071])).
% 1.55/1.74 tff(6090,plain,
% 1.55/1.74 (b(s(s(s(z))), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1090, 6089])).
% 1.55/1.74 tff(6091,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[5868, 233, 273, 272, 1072, 402])).
% 1.55/1.74 tff(6092,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(6093,plain,
% 1.55/1.74 (~b(s(z), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6092, 6090, 5920, 6025])).
% 1.55/1.74 tff(6094,plain,
% 1.55/1.74 (r(s(z), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[260, 6093])).
% 1.55/1.74 tff(6095,plain,
% 1.55/1.74 (~r(s(z), s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2971, 108, 6031, 6027, 6094])).
% 1.55/1.74 tff(6096,plain,
% 1.55/1.74 (b(s(z), s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2414, 6095])).
% 1.55/1.74 tff(6097,plain,
% 1.55/1.74 (~r(s(s(z)), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2963, 108, 6031, 6027, 6094])).
% 1.55/1.74 tff(6098,plain,
% 1.55/1.74 (b(s(s(z)), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[50, 6097])).
% 1.55/1.74 tff(6099,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2986, 6098, 6096, 80, 6090])).
% 1.55/1.74 tff(6100,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(6101,plain,
% 1.55/1.74 (~b(s(s(z)), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[6100, 130, 81, 284])).
% 1.55/1.74 tff(6102,plain,
% 1.55/1.74 (r(s(s(z)), s(s(s(z))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2228, 6101])).
% 1.55/1.74 tff(6103,plain,
% 1.55/1.74 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2598, 6102, 81, 130])).
% 1.55/1.74 tff(6104,plain,
% 1.55/1.74 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[440, 6103])).
% 1.55/1.74 tff(6105,plain,
% 1.55/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(6106,plain,
% 1.55/1.74 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6107,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[6106])).
% 1.55/1.75 tff(6108,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)))),
% 1.55/1.75 inference(transitivity,[status(thm)],[6107, 6105])).
% 1.55/1.75 tff(6109,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6110,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6109, 6108])).
% 1.55/1.75 tff(6111,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6110, 233, 273, 1072, 388, 402])).
% 1.55/1.75 tff(6112,plain,((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(6113,plain,
% 1.55/1.75 (~b(z, s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6112, 402, 1072, 273])).
% 1.55/1.75 tff(6114,plain,
% 1.55/1.75 (r(z, s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[128, 6113])).
% 1.55/1.75 tff(6115,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6116,plain,
% 1.55/1.75 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6117,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[6116])).
% 1.55/1.75 tff(6118,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[6117, 6115])).
% 1.55/1.75 tff(6119,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6120,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6119, 6118])).
% 1.55/1.75 tff(6121,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6120, 108, 978, 3244, 52, 98])).
% 1.55/1.75 tff(6122,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(6123,plain,
% 1.55/1.75 (~r(z, s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6122, 6114, 52, 3244])).
% 1.55/1.75 tff(6124,plain,
% 1.55/1.75 (b(z, s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[222, 6123])).
% 1.55/1.75 tff(6125,plain,
% 1.55/1.75 (~b(s(s(s(z))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6092, 402, 1072, 273])).
% 1.55/1.75 tff(6126,plain,
% 1.55/1.75 (r(s(s(s(z))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[244, 6125])).
% 1.55/1.75 tff(6127,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6128,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6129,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6128, 6127])).
% 1.55/1.75 tff(6130,plain,
% 1.55/1.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6129, 108, 6126, 3244, 6114])).
% 1.55/1.75 tff(6131,plain,
% 1.55/1.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[386, 6130])).
% 1.55/1.75 tff(6132,plain,
% 1.55/1.75 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6133,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[6132])).
% 1.55/1.75 tff(6134,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[6133, 1183])).
% 1.55/1.75 tff(6135,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6136,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6135, 6134])).
% 1.55/1.75 tff(6137,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6136, 233, 6131, 273, 6124, 204])).
% 1.55/1.75 tff(6138,plain,((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(6139,plain,
% 1.55/1.75 (~b(s(z), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6138, 1072, 204, 3244, 52, 273])).
% 1.55/1.75 tff(6140,plain,
% 1.55/1.75 (r(s(z), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[260, 6139])).
% 1.55/1.75 tff(6141,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6142,plain,
% 1.55/1.75 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6143,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[6142])).
% 1.55/1.75 tff(6144,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[6143, 6141])).
% 1.55/1.75 tff(6145,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6146,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6145, 6144])).
% 1.55/1.75 tff(6147,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6146, 108, 978, 3244, 52, 246])).
% 1.55/1.75 tff(6148,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(6149,plain,
% 1.55/1.75 (~r(z, s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6148, 6140, 52, 3244])).
% 1.55/1.75 tff(6150,plain,
% 1.55/1.75 (b(z, s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[222, 6149])).
% 1.55/1.75 tff(6151,plain,
% 1.55/1.75 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[5968, 6150, 273, 204])).
% 1.55/1.75 tff(6152,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[462, 6151])).
% 1.55/1.75 tff(6153,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6154,plain,
% 1.55/1.75 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6155,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[6154])).
% 1.55/1.75 tff(6156,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[6155, 6153])).
% 1.55/1.75 tff(6157,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6158,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6157, 6156])).
% 1.55/1.75 tff(6159,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6158, 233, 389, 273, 272, 1930])).
% 1.55/1.75 tff(6160,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(6161,plain,
% 1.55/1.75 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6160, 272, 273, 6150])).
% 1.55/1.75 tff(6162,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[386, 6161])).
% 1.55/1.75 tff(6163,plain,
% 1.55/1.75 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3996, 272, 6150, 204])).
% 1.55/1.75 tff(6164,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[462, 6163])).
% 1.55/1.75 tff(6165,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6166,plain,
% 1.55/1.75 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6167,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[6166])).
% 1.55/1.75 tff(6168,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[6167, 6165])).
% 1.55/1.75 tff(6169,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6170,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6169, 6168])).
% 1.55/1.75 tff(6171,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6170, 108, 130, 492, 2240, 680])).
% 1.55/1.75 tff(6172,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(6173,plain,
% 1.55/1.75 (~r(s(s(s(z))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6172, 6164, 2240, 6162])).
% 1.55/1.75 tff(6174,plain,
% 1.55/1.75 (b(s(s(s(z))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[340, 6173])).
% 1.55/1.75 tff(6175,plain,
% 1.55/1.75 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3374, 6174, 3244, 2240, 273, 204])).
% 1.55/1.75 tff(6176,plain,
% 1.55/1.75 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1894, 6174, 52, 1072, 6162])).
% 1.55/1.75 tff(6177,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[440, 6176, 6175])).
% 1.55/1.75 tff(6178,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(6179,plain,
% 1.55/1.75 (~b(s(s(s(z))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[6178, 1072, 52, 3244, 4305, 273, 204])).
% 1.55/1.75 tff(6180,plain,
% 1.55/1.75 (z = elem!1),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[5903, 284, 3244, 4303])).
% 1.55/1.75 tff(6181,plain,
% 1.55/1.75 (elem!1 = z),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1056, 6180])).
% 1.55/1.75 tff(6182,plain,
% 1.55/1.75 (~b(s(s(s(z))), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3707, 6181, 3701])).
% 1.55/1.75 tff(6183,plain,
% 1.55/1.75 (r(s(s(s(z))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[244, 3701])).
% 1.55/1.75 tff(6184,plain,
% 1.55/1.75 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3374, 284, 3244, 4305, 273, 204])).
% 1.55/1.75 tff(6185,plain,
% 1.55/1.75 (r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[440, 6184])).
% 1.55/1.75 tff(6186,plain,
% 1.55/1.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[2586, 6185, 4305, 6183])).
% 1.55/1.75 tff(6187,plain,
% 1.55/1.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[386, 6186])).
% 1.55/1.75 tff(6188,plain,
% 1.55/1.75 (b(elem!1, s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1746, 6181, 273])).
% 1.55/1.75 tff(6189,plain,
% 1.55/1.75 (~b(s(s(s(s(z)))), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1080, 6187, 1072, 6188])).
% 1.55/1.75 tff(6190,plain,
% 1.55/1.75 (~(elem!1 = s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[830, 6189, 6187])).
% 1.55/1.75 tff(6191,plain,
% 1.55/1.75 (~(s(s(s(z))) = elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[838, 6190])).
% 1.55/1.75 tff(6192,plain,
% 1.55/1.75 (~r(z, s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3276, 680, 3244, 4305])).
% 1.55/1.75 tff(6193,plain,
% 1.55/1.75 (b(z, s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[359, 6192])).
% 1.55/1.75 tff(6194,plain,
% 1.55/1.75 (~b(s(s(z)), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[4543, 284, 6193, 273])).
% 1.55/1.75 tff(6195,plain,
% 1.55/1.75 (~(s(s(z)) = elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[5434, 6182, 284])).
% 1.55/1.75 tff(6196,plain,
% 1.55/1.75 (r(s(s(z)), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1175, 6195, 6194])).
% 1.55/1.75 tff(6197,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.55/1.75 tff(6198,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6199,plain,
% 1.55/1.75 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(6200,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[6199])).
% 1.55/1.75 tff(6201,plain,
% 1.55/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[6200, 6198])).
% 1.55/1.75 tff(6202,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(6203,plain,
% 1.55/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[6202, 6201])).
% 1.55/1.76 tff(6204,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6203, 233, 389, 6197, 284, 919])).
% 1.55/1.76 tff(6205,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6206,plain,
% 1.55/1.76 (~b(elem!1, s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6205, 6187, 284, 6188])).
% 1.55/1.76 tff(6207,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6208,plain,
% 1.55/1.76 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6209,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6208])).
% 1.55/1.76 tff(6210,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.55/1.76 inference(transitivity,[status(thm)],[6209, 6207])).
% 1.55/1.76 tff(6211,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(6212,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[6211, 6210])).
% 1.55/1.76 tff(6213,plain,
% 1.55/1.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6212, 108, 1213, 861, 851])).
% 1.55/1.76 tff(6214,plain,
% 1.55/1.76 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[440, 6213])).
% 1.55/1.76 tff(6215,plain,
% 1.55/1.76 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.55/1.76 inference(symmetry,[status(thm)],[143])).
% 1.55/1.76 tff(6216,plain,
% 1.55/1.76 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6215])).
% 1.55/1.76 tff(6217,plain,
% 1.55/1.76 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[169, 6216])).
% 1.55/1.76 tff(6218,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6219,plain,
% 1.55/1.76 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6220,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6219])).
% 1.55/1.76 tff(6221,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.76 inference(transitivity,[status(thm)],[6220, 6218])).
% 1.55/1.76 tff(6222,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(6223,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[6222, 6221])).
% 1.55/1.76 tff(6224,plain,
% 1.55/1.76 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6223, 108, 1213, 861, 851])).
% 1.55/1.76 tff(6225,plain,
% 1.55/1.76 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[460, 45, 6224])).
% 1.55/1.76 tff(6226,plain,
% 1.55/1.76 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6225, 6217])).
% 1.55/1.76 tff(6227,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[5839, 233, 389, 284, 6226, 6214])).
% 1.55/1.76 tff(6228,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6229,plain,
% 1.55/1.76 (elem!1 = s(s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6228, 6206, 284, 6187, 6189, 6196])).
% 1.55/1.76 tff(6230,plain,
% 1.55/1.76 (s(s(s(s(z)))) = elem!1),
% 1.55/1.76 inference(symmetry,[status(thm)],[874])).
% 1.55/1.76 tff(6231,plain,
% 1.55/1.76 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6230])).
% 1.55/1.76 tff(6232,plain,
% 1.55/1.76 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.76 inference(symmetry,[status(thm)],[6231])).
% 1.55/1.76 tff(6233,plain,
% 1.55/1.76 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[862, 6232])).
% 1.55/1.76 tff(6234,plain,
% 1.55/1.76 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2465, 108, 2240, 680, 491])).
% 1.55/1.76 tff(6235,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6234, 6233])).
% 1.55/1.76 tff(6236,plain,((~r(s(s(s(z))), elem!1)) | (~(elem!1 = s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6237,plain,
% 1.55/1.76 (~r(s(s(s(z))), elem!1)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6236, 6229, 4305, 6185, 680])).
% 1.55/1.76 tff(6238,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[843, 6237, 6191, 6182])).
% 1.55/1.76 tff(6239,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), z) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6240,plain,
% 1.55/1.76 (~b(s(s(s(z))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6239, 6152, 1072, 273, 6179, 3244, 204, 4303])).
% 1.55/1.76 tff(6241,plain,
% 1.55/1.76 (r(s(s(s(z))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[340, 6240])).
% 1.55/1.76 tff(6242,plain,
% 1.55/1.76 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6172, 6241, 4305, 6152])).
% 1.55/1.76 tff(6243,plain,
% 1.55/1.76 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[386, 6242])).
% 1.55/1.76 tff(6244,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1188, 233, 6243, 273, 6150, 204])).
% 1.55/1.76 tff(6245,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6246,plain,
% 1.55/1.76 (~b(s(s(s(z))), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6245, 204, 273, 3244, 4303, 52])).
% 1.55/1.76 tff(6247,plain,
% 1.55/1.76 (r(s(s(s(z))), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1090, 6246])).
% 1.55/1.76 tff(6248,plain,
% 1.55/1.76 (~r(s(s(z)), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2540, 6247, 4305, 52])).
% 1.55/1.76 tff(6249,plain,
% 1.55/1.76 (b(s(s(z)), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[50, 6248])).
% 1.55/1.76 tff(6250,plain,
% 1.55/1.76 (~r(s(s(z)), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2540, 92, 2240, 52])).
% 1.55/1.76 tff(6251,plain,
% 1.55/1.76 (b(s(s(z)), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[50, 6250])).
% 1.55/1.76 tff(6252,plain,
% 1.55/1.76 (~b(s(s(s(z))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[334, 130, 52, 92, 273, 247])).
% 1.55/1.76 tff(6253,plain,
% 1.55/1.76 (~r(s(s(s(z))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6172, 130, 2240, 680])).
% 1.55/1.76 tff(6254,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[340, 6253, 6252])).
% 1.55/1.76 tff(6255,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6256,plain,
% 1.55/1.76 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6255, 680, 2240, 52, 92, 273, 247])).
% 1.55/1.76 tff(6257,plain,
% 1.55/1.76 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[386, 6256])).
% 1.55/1.76 tff(6258,plain,
% 1.55/1.76 (~b(z, s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1188, 233, 6257, 273, 204])).
% 1.55/1.76 tff(6259,plain,
% 1.55/1.76 (r(z, s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[222, 6258])).
% 1.55/1.76 tff(6260,plain,
% 1.55/1.76 (~r(s(z), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[986, 6259, 247, 92])).
% 1.55/1.76 tff(6261,plain,
% 1.55/1.76 (b(s(z), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[260, 6260])).
% 1.55/1.76 tff(6262,plain,
% 1.55/1.76 (~r(z, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6122, 6259, 52, 3244])).
% 1.55/1.76 tff(6263,plain,
% 1.55/1.76 (b(z, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[128, 6262])).
% 1.55/1.76 tff(6264,plain,
% 1.55/1.76 (~r(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[3276, 680, 3244, 2240])).
% 1.55/1.76 tff(6265,plain,
% 1.55/1.76 (b(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[359, 6264])).
% 1.55/1.76 tff(6266,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6267,plain,
% 1.55/1.76 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6268,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6267])).
% 1.55/1.76 tff(6269,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(transitivity,[status(thm)],[6268, 6266])).
% 1.55/1.76 tff(6270,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(6271,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[6270, 6269])).
% 1.55/1.76 tff(6272,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6271, 233, 6265, 6263, 6261, 6251])).
% 1.55/1.76 tff(6273,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6274,plain,
% 1.55/1.76 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6273, 247, 3244, 52, 92, 273, 204, 2240])).
% 1.55/1.76 tff(6275,plain,
% 1.55/1.76 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[462, 6274])).
% 1.55/1.76 tff(6276,plain,
% 1.55/1.76 (~b(z, s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[5968, 6275, 273, 204])).
% 1.55/1.76 tff(6277,plain,
% 1.55/1.76 (r(z, s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[222, 6276])).
% 1.55/1.76 tff(6278,plain,
% 1.55/1.76 (~r(s(z), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[986, 6277, 247, 92])).
% 1.55/1.76 tff(6279,plain,
% 1.55/1.76 (b(s(z), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[260, 6278])).
% 1.55/1.76 tff(6280,plain,
% 1.55/1.76 (~r(z, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6122, 6277, 52, 3244])).
% 1.55/1.76 tff(6281,plain,
% 1.55/1.76 (b(z, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[128, 6280])).
% 1.55/1.76 tff(6282,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6283,plain,
% 1.55/1.76 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6284,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6283])).
% 1.55/1.76 tff(6285,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(transitivity,[status(thm)],[6284, 6282])).
% 1.55/1.76 tff(6286,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(6287,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[6286, 6285])).
% 1.55/1.76 tff(6288,plain,
% 1.55/1.76 (~b(s(s(z)), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6287, 233, 6281, 6279, 6251])).
% 1.55/1.76 tff(6289,plain,
% 1.55/1.76 (r(s(s(z)), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[374, 6288])).
% 1.55/1.76 tff(6290,plain,
% 1.55/1.76 (~b(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6271, 233, 6281, 6279, 6251])).
% 1.55/1.76 tff(6291,plain,
% 1.55/1.76 (r(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[359, 6290])).
% 1.55/1.76 tff(6292,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2634, 6291, 6289, 2240, 247])).
% 1.55/1.76 tff(6293,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(6294,plain,
% 1.55/1.76 (~r(s(s(s(z))), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6293, 6247, 52, 3244, 4305, 273, 204])).
% 1.55/1.76 tff(6295,plain,
% 1.55/1.76 (b(s(s(s(z))), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[244, 6294])).
% 1.55/1.76 tff(6296,plain,
% 1.55/1.76 (~r(s(s(s(z))), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6293, 92, 52, 3244, 2240, 273, 204])).
% 1.55/1.76 tff(6297,plain,
% 1.55/1.76 (b(s(s(s(z))), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[244, 6296])).
% 1.55/1.76 tff(6298,plain,
% 1.55/1.76 (~b(z, s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[3996, 442, 6297, 204])).
% 1.55/1.76 tff(6299,plain,
% 1.55/1.76 (r(z, s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[222, 6298])).
% 1.55/1.76 tff(6300,plain,
% 1.55/1.76 (~r(s(z), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6148, 6299, 52, 3244])).
% 1.55/1.76 tff(6301,plain,
% 1.55/1.76 (b(s(z), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[260, 6300])).
% 1.55/1.76 tff(6302,plain,
% 1.55/1.76 (~r(z, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6122, 6299, 52, 3244])).
% 1.55/1.76 tff(6303,plain,
% 1.55/1.76 (b(z, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[128, 6302])).
% 1.55/1.76 tff(6304,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6305,plain,
% 1.55/1.76 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6306,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6305])).
% 1.55/1.76 tff(6307,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.55/1.76 inference(transitivity,[status(thm)],[6306, 6304])).
% 1.55/1.76 tff(6308,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(6309,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[6308, 6307])).
% 1.55/1.76 tff(6310,plain,
% 1.55/1.76 (~b(s(z), s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6309, 233, 6297, 6303, 6301])).
% 1.55/1.76 tff(6311,plain,
% 1.55/1.76 (r(s(z), s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[325, 6310])).
% 1.55/1.76 tff(6312,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6313,plain,
% 1.55/1.76 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6314,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[6313])).
% 1.55/1.76 tff(6315,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 1.55/1.76 inference(transitivity,[status(thm)],[6314, 6312])).
% 1.55/1.76 tff(6316,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(6317,plain,
% 1.55/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 1.55/1.76 tff(6318,plain,
% 1.55/1.76 (~b(s(s(z)), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6317, 233, 273, 6297, 6303, 6301, 6251])).
% 1.55/1.76 tff(6319,plain,
% 1.55/1.76 (r(s(s(z)), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[374, 6318])).
% 1.55/1.76 tff(6320,plain,
% 1.55/1.76 (~b(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6271, 233, 6303, 6301, 6251])).
% 1.55/1.76 tff(6321,plain,
% 1.55/1.76 (r(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[359, 6320])).
% 1.55/1.76 tff(6322,plain,
% 1.55/1.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[3444, 6321, 3244, 6319])).
% 1.55/1.76 tff(6323,plain,
% 1.55/1.76 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[440, 6322])).
% 1.55/1.76 tff(6324,plain,
% 1.55/1.76 (~b(s(s(s(z))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[3374, 6323, 3244, 2240, 273, 204])).
% 1.55/1.76 tff(6325,plain,
% 1.55/1.76 (r(s(s(s(z))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[340, 6324])).
% 1.55/1.76 tff(6326,plain,
% 1.55/1.76 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2316, 108, 492, 2240, 1537])).
% 1.55/1.76 tff(6327,plain,
% 1.55/1.76 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[535, 45, 532, 6326])).
% 1.55/1.76 tff(6328,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6329,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(6330,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[6329, 6328])).
% 1.55/1.76 tff(6331,plain,
% 1.55/1.76 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6330, 108, 492, 2337, 1537])).
% 1.55/1.76 tff(6332,plain,
% 1.55/1.76 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[3933, 6331])).
% 1.55/1.76 tff(6333,plain,
% 1.55/1.76 (~r(s(z), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[4130, 108, 492, 2240, 2337])).
% 1.55/1.76 tff(6334,plain,
% 1.55/1.76 (b(s(z), s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2414, 6333])).
% 1.55/1.76 tff(6335,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6336,plain,
% 1.55/1.76 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(6337,plain,
% 1.55/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6336])).
% 1.55/1.77 tff(6338,plain,
% 1.55/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[6337, 6335])).
% 1.55/1.77 tff(6339,plain,
% 1.55/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(6340,plain,
% 1.55/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6339, 6338])).
% 1.55/1.77 tff(6341,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6340, 233, 442, 424, 6334, 6332, 519, 6327])).
% 1.55/1.77 tff(6342,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(6343,plain,
% 1.55/1.77 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6342, 442, 6323, 6251, 6325, 6311, 2240])).
% 1.55/1.77 tff(6344,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[598, 6343])).
% 1.55/1.77 tff(6345,plain,
% 1.55/1.77 (~b(s(s(s(s(s(z))))), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2701, 233, 273, 6297, 6344])).
% 1.55/1.77 tff(6346,plain,
% 1.55/1.77 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[517, 45, 514, 6345])).
% 1.55/1.77 tff(6347,plain,
% 1.55/1.77 (~r(s(z), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[4130, 108, 6325, 2240, 6311])).
% 1.55/1.77 tff(6348,plain,
% 1.55/1.77 (b(s(z), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2414, 6347])).
% 1.55/1.77 tff(6349,plain,
% 1.55/1.77 (~b(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2981, 6348, 442, 6251])).
% 1.55/1.77 tff(6350,plain,
% 1.55/1.77 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[200, 45, 6349])).
% 1.55/1.77 tff(6351,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6350, 96])).
% 1.55/1.77 tff(6352,plain,
% 1.55/1.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[196, 6351, 52, 92])).
% 1.55/1.77 tff(6353,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[386, 6352])).
% 1.55/1.77 tff(6354,plain,
% 1.55/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6355,plain,
% 1.55/1.77 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6356,plain,
% 1.55/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6355])).
% 1.55/1.77 tff(6357,plain,
% 1.55/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[6356, 6354])).
% 1.55/1.77 tff(6358,plain,
% 1.55/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(6359,plain,
% 1.55/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6358, 6357])).
% 1.55/1.77 tff(6360,plain,
% 1.55/1.77 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6359, 233, 6353, 6297, 6344])).
% 1.55/1.77 tff(6361,plain,
% 1.55/1.77 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[579, 45, 576, 6360])).
% 1.55/1.77 tff(6362,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6363,plain,
% 1.55/1.77 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6364,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6363])).
% 1.55/1.77 tff(6365,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[6364, 6362])).
% 1.55/1.77 tff(6366,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(6367,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6366, 6365])).
% 1.55/1.77 tff(6368,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6367, 108, 6299, 3244, 6361, 6346])).
% 1.55/1.77 tff(6369,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(6370,plain,
% 1.55/1.77 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6369, 6247, 273, 4305, 52, 3244, 204])).
% 1.55/1.77 tff(6371,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[462, 6370])).
% 1.55/1.77 tff(6372,plain,
% 1.55/1.77 (b(s(s(s(z))), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[340, 6253])).
% 1.55/1.77 tff(6373,plain,
% 1.55/1.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[4326, 130, 2240, 92])).
% 1.55/1.77 tff(6374,plain,
% 1.55/1.77 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[440, 6373])).
% 1.55/1.77 tff(6375,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[3374, 6374, 6372, 3244, 2240, 273, 204])).
% 1.55/1.77 tff(6376,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(6377,plain,
% 1.55/1.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6376, 204, 4305, 273, 3244, 6247, 6371])).
% 1.55/1.77 tff(6378,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[386, 6377])).
% 1.55/1.77 tff(6379,plain,
% 1.55/1.77 (~b(z, s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6160, 6378, 273, 6295])).
% 1.55/1.77 tff(6380,plain,
% 1.55/1.77 (r(z, s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[222, 6379])).
% 1.55/1.77 tff(6381,plain,
% 1.55/1.77 (~r(s(z), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6148, 6380, 52, 3244])).
% 1.55/1.77 tff(6382,plain,
% 1.55/1.77 (b(s(z), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[260, 6381])).
% 1.55/1.77 tff(6383,plain,
% 1.55/1.77 (~r(z, s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6122, 6380, 52, 3244])).
% 1.55/1.77 tff(6384,plain,
% 1.55/1.77 (b(z, s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[128, 6383])).
% 1.55/1.77 tff(6385,plain,
% 1.55/1.77 (~r(z, s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[3276, 6371, 3244, 4305])).
% 1.55/1.77 tff(6386,plain,
% 1.55/1.77 (b(z, s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[359, 6385])).
% 1.55/1.77 tff(6387,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6271, 233, 6386, 6384, 6382, 6249])).
% 1.55/1.77 tff(6388,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(6389,plain,
% 1.55/1.77 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6388, 52, 3244, 273, 4303])).
% 1.55/1.77 tff(6390,plain,
% 1.55/1.77 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[186, 6389])).
% 1.55/1.77 tff(6391,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6392,plain,
% 1.55/1.77 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6393,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6392])).
% 1.55/1.77 tff(6394,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[6393, 6391])).
% 1.55/1.77 tff(6395,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(6396,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6395, 6394])).
% 1.55/1.77 tff(6397,plain,
% 1.55/1.77 (~r(s(z), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6396, 108, 6390, 3244, 52])).
% 1.55/1.77 tff(6398,plain,
% 1.55/1.77 (b(s(z), s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[325, 6397])).
% 1.55/1.77 tff(6399,plain,
% 1.55/1.77 (~r(s(s(s(z))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[4152, 6390, 3244, 52])).
% 1.55/1.77 tff(6400,plain,
% 1.55/1.77 (b(s(s(s(z))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1090, 6399])).
% 1.55/1.77 tff(6401,plain,
% 1.55/1.77 (~b(s(z), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2195, 233, 273, 6400, 6398])).
% 1.55/1.77 tff(6402,plain,
% 1.55/1.77 (r(s(z), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[260, 6401])).
% 1.55/1.77 tff(6403,plain,
% 1.55/1.77 (~b(z, s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2203, 233, 273, 6400, 6398])).
% 1.55/1.77 tff(6404,plain,
% 1.55/1.77 (r(z, s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[128, 6403])).
% 1.55/1.77 tff(6405,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6406,plain,
% 1.55/1.77 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6407,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6406])).
% 1.55/1.77 tff(6408,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[6407, 6405])).
% 1.55/1.77 tff(6409,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(6410,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6409, 6408])).
% 1.55/1.77 tff(6411,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6410, 108, 3244, 52, 6404, 6402])).
% 1.55/1.77 tff(6412,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(6413,plain,
% 1.55/1.77 (~r(s(z), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[6412, 6101, 5920, 5995])).
% 1.55/1.77 tff(6414,plain,
% 1.55/1.77 (b(s(z), s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1122, 6413])).
% 1.55/1.77 tff(6415,plain,
% 1.55/1.77 (z = elem!1),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[5903, 6101, 5995, 284])).
% 1.55/1.77 tff(6416,plain,
% 1.55/1.77 (s(z) = s(elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6415])).
% 1.55/1.77 tff(6417,plain,
% 1.55/1.77 (s(s(z)) = s(s(elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6416])).
% 1.55/1.77 tff(6418,plain,
% 1.55/1.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6417])).
% 1.55/1.77 tff(6419,plain,
% 1.55/1.77 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6418])).
% 1.55/1.77 tff(6420,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6419, 6416])).
% 1.55/1.77 tff(6421,plain,
% 1.55/1.77 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6420])).
% 1.55/1.77 tff(6422,plain,
% 1.55/1.77 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(z)))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6421])).
% 1.55/1.77 tff(6423,plain,
% 1.55/1.77 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6419])).
% 1.55/1.77 tff(6424,plain,
% 1.55/1.77 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6423])).
% 1.55/1.77 tff(6425,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.55/1.77 inference(symmetry,[status(thm)],[6424])).
% 1.55/1.77 tff(6426,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6415])).
% 1.55/1.77 tff(6427,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[5995, 6426])).
% 1.55/1.77 tff(6428,plain,
% 1.55/1.77 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6427, 6425])).
% 1.55/1.77 tff(6429,plain,
% 1.55/1.77 (s(elem!1) = s(z)),
% 1.55/1.77 inference(symmetry,[status(thm)],[6416])).
% 1.55/1.77 tff(6430,plain,
% 1.55/1.77 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6429])).
% 1.55/1.77 tff(6431,plain,
% 1.55/1.77 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.55/1.77 inference(symmetry,[status(thm)],[6430])).
% 1.55/1.77 tff(6432,plain,
% 1.55/1.77 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6415])).
% 1.55/1.77 tff(6433,plain,
% 1.55/1.77 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6432])).
% 1.55/1.77 tff(6434,plain,
% 1.55/1.77 (~(s(z) = elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[122, 6433])).
% 1.55/1.77 tff(6435,plain,
% 1.55/1.77 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6429])).
% 1.55/1.77 tff(6436,plain,
% 1.55/1.77 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6435])).
% 1.55/1.77 tff(6437,plain,
% 1.55/1.77 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6429])).
% 1.55/1.77 tff(6438,plain,
% 1.55/1.77 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6437])).
% 1.55/1.77 tff(6439,plain,
% 1.55/1.77 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6417, 6418])).
% 1.55/1.77 tff(6440,plain,
% 1.55/1.77 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6102, 6439])).
% 1.55/1.77 tff(6441,plain,
% 1.55/1.77 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6418])).
% 1.55/1.77 tff(6442,plain,
% 1.55/1.77 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6423, 6441])).
% 1.55/1.77 tff(6443,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6442])).
% 1.55/1.77 tff(6444,plain,
% 1.55/1.77 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[130, 6443])).
% 1.55/1.77 tff(6445,plain,
% 1.55/1.77 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6423])).
% 1.55/1.77 tff(6446,plain,
% 1.55/1.77 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6445])).
% 1.55/1.77 tff(6447,plain,
% 1.55/1.77 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6418])).
% 1.55/1.77 tff(6448,plain,
% 1.55/1.77 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[81, 6447])).
% 1.55/1.77 tff(6449,plain,
% 1.55/1.77 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[6448, 6446])).
% 1.55/1.77 tff(6450,plain,
% 1.55/1.77 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[1723])).
% 1.55/1.77 tff(6451,plain,
% 1.55/1.77 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6450])).
% 1.55/1.77 tff(6452,plain,
% 1.55/1.77 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[1725])).
% 1.55/1.77 tff(6453,plain,
% 1.55/1.77 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 1.55/1.77 inference(symmetry,[status(thm)],[6452])).
% 1.55/1.77 tff(6454,plain,
% 1.55/1.77 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.55/1.77 inference(transitivity,[status(thm)],[6453, 6451])).
% 1.55/1.77 tff(6455,plain,
% 1.55/1.77 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(z)), s(z)))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[6454])).
% 1.55/1.77 tff(6456,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.55/1.77 tff(6457,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.55/1.77 tff(6458,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6459,plain,
% 1.55/1.77 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(6460,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6459])).
% 1.55/1.78 tff(6461,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[6460, 6458])).
% 1.55/1.78 tff(6462,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(6463,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6462, 6461])).
% 1.55/1.78 tff(6464,plain,
% 1.55/1.78 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6463, 108, 5238, 6457])).
% 1.55/1.78 tff(6465,plain,
% 1.55/1.78 (~r(s(s(elem!1)), s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6464, 6456])).
% 1.55/1.78 tff(6466,plain,
% 1.55/1.78 (~r(s(s(z)), s(z))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6465, 6455])).
% 1.55/1.78 tff(6467,plain,
% 1.55/1.78 (b(s(s(z)), s(z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[50, 6466])).
% 1.55/1.78 tff(6468,plain,
% 1.55/1.78 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[2905, 1723])).
% 1.55/1.78 tff(6469,plain,
% 1.55/1.78 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.55/1.78 inference(symmetry,[status(thm)],[6468])).
% 1.55/1.78 tff(6470,plain,
% 1.55/1.78 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(z)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6469])).
% 1.55/1.78 tff(6471,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.55/1.78 tff(6472,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6473,plain,
% 1.55/1.78 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6474,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6473])).
% 1.55/1.78 tff(6475,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[6474, 6472])).
% 1.55/1.78 tff(6476,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(6477,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6476, 6475])).
% 1.55/1.78 tff(6478,plain,
% 1.55/1.78 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6477, 108, 6457, 6471])).
% 1.55/1.78 tff(6479,plain,
% 1.55/1.78 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6478, 6456])).
% 1.55/1.78 tff(6480,plain,
% 1.55/1.78 (~r(s(s(s(s(z)))), s(z))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6479, 6470])).
% 1.55/1.78 tff(6481,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), s(z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[4293, 6480])).
% 1.55/1.78 tff(6482,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6483,plain,
% 1.55/1.78 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6484,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6483])).
% 1.55/1.78 tff(6485,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[6484, 6482])).
% 1.55/1.78 tff(6486,plain,
% 1.55/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(6487,plain,
% 1.55/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6486, 6485])).
% 1.55/1.78 tff(6488,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6487, 233, 424, 2854, 519, 203])).
% 1.55/1.78 tff(6489,plain,((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6490,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6489, 6481, 6467, 2854, 424])).
% 1.55/1.78 tff(6491,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6492,plain,
% 1.55/1.78 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6491, 6414, 6104, 6415, 6449, 6444, 6440])).
% 1.55/1.78 tff(6493,plain,
% 1.55/1.78 (~r(s(z), s(s(s(elem!1))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6492, 6438])).
% 1.55/1.78 tff(6494,plain,
% 1.55/1.78 (b(s(z), s(s(s(elem!1))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1441, 6493])).
% 1.55/1.78 tff(6495,plain,
% 1.55/1.78 (b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6494, 6436])).
% 1.55/1.78 tff(6496,plain,
% 1.55/1.78 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6441])).
% 1.55/1.78 tff(6497,plain,
% 1.55/1.78 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.55/1.78 inference(symmetry,[status(thm)],[6496])).
% 1.55/1.78 tff(6498,plain,
% 1.55/1.78 (elem!1 = z),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1056, 6415])).
% 1.55/1.78 tff(6499,plain,
% 1.55/1.78 (b(s(s(s(z))), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[272, 3703])).
% 1.55/1.78 tff(6500,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[797, 6499])).
% 1.55/1.78 tff(6501,plain,((~(elem!1 = z)) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6502,plain,
% 1.55/1.78 (b(s(s(s(z))), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6501, 6498, 6025])).
% 1.55/1.78 tff(6503,plain,
% 1.55/1.78 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6502, 6497])).
% 1.55/1.78 tff(6504,plain,
% 1.55/1.78 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6418])).
% 1.55/1.78 tff(6505,plain,
% 1.55/1.78 (b(elem!1, s(s(s(z))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1746, 6498, 5920])).
% 1.55/1.78 tff(6506,plain,
% 1.55/1.78 (b(elem!1, s(s(s(elem!1))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6505, 6504])).
% 1.55/1.78 tff(6507,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6508,plain,
% 1.55/1.78 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6509,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6508])).
% 1.55/1.78 tff(6510,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.55/1.78 inference(transitivity,[status(thm)],[6509, 6507])).
% 1.55/1.78 tff(6511,plain,
% 1.55/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(6512,plain,
% 1.55/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6511, 6510])).
% 1.55/1.78 tff(6513,plain,
% 1.55/1.78 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6512, 233, 6506, 6503])).
% 1.55/1.78 tff(6514,plain,
% 1.55/1.78 (~b(s(elem!1), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6513, 6495])).
% 1.55/1.78 tff(6515,plain,
% 1.55/1.78 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[1723])).
% 1.55/1.78 tff(6516,plain,
% 1.55/1.78 (b(s(elem!1), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[1102, 6515])).
% 1.55/1.78 tff(6517,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[5083, 6516])).
% 1.55/1.78 tff(6518,plain,((~b(s(z), elem!1)) | b(s(elem!1), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6519,plain,
% 1.55/1.78 (~b(s(z), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6518, 6514, 6415])).
% 1.55/1.78 tff(6520,plain,
% 1.55/1.78 (r(s(z), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1130, 6519, 6434])).
% 1.55/1.78 tff(6521,plain,
% 1.55/1.78 (r(s(elem!1), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6520, 6431])).
% 1.55/1.78 tff(6522,plain,
% 1.55/1.78 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.55/1.78 inference(symmetry,[status(thm)],[951])).
% 1.55/1.78 tff(6523,plain,
% 1.55/1.78 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.55/1.78 inference(transitivity,[status(thm)],[6432, 6522])).
% 1.55/1.78 tff(6524,plain,
% 1.55/1.78 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6523])).
% 1.55/1.78 tff(6525,plain,
% 1.55/1.78 (~(elem!1 = s(z))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[122, 6524])).
% 1.55/1.78 tff(6526,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.55/1.78 tff(6527,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6528,plain,
% 1.55/1.78 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6529,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6528])).
% 1.55/1.78 tff(6530,plain,
% 1.55/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[6529, 6527])).
% 1.55/1.78 tff(6531,plain,
% 1.55/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(6532,plain,
% 1.55/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6531, 6530])).
% 1.55/1.78 tff(6533,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6532, 233, 1460, 967, 6526, 1419])).
% 1.55/1.78 tff(6534,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6535,plain,
% 1.55/1.78 (~b(elem!1, s(z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6534, 6494, 6503, 6506])).
% 1.55/1.78 tff(6536,plain,
% 1.55/1.78 (r(elem!1, s(z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[965, 6535, 6525])).
% 1.55/1.78 tff(6537,plain,
% 1.55/1.78 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[1724])).
% 1.55/1.78 tff(6538,plain,
% 1.55/1.78 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.55/1.78 inference(symmetry,[status(thm)],[6537])).
% 1.55/1.78 tff(6539,plain,
% 1.55/1.78 (r(elem!1, s(elem!1))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[1389, 6538])).
% 1.55/1.78 tff(6540,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[5105, 6539])).
% 1.55/1.78 tff(6541,plain,((~r(elem!1, s(z))) | r(elem!1, s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6542,plain,
% 1.55/1.78 (r(elem!1, s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6541, 6536, 6415])).
% 1.55/1.78 tff(6543,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6544,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(6545,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6544, 6543])).
% 1.55/1.78 tff(6546,plain,
% 1.55/1.78 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6545, 108, 6542, 6521, 6428])).
% 1.55/1.78 tff(6547,plain,
% 1.55/1.78 (~r(s(s(s(s(z)))), s(z))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6546, 6422])).
% 1.55/1.78 tff(6548,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), s(z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[4293, 6547])).
% 1.55/1.78 tff(6549,plain,
% 1.55/1.78 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6416])).
% 1.55/1.78 tff(6550,plain,
% 1.55/1.78 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.55/1.78 inference(symmetry,[status(thm)],[6549])).
% 1.55/1.78 tff(6551,plain,
% 1.55/1.78 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6417])).
% 1.55/1.78 tff(6552,plain,
% 1.55/1.78 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 1.55/1.78 inference(symmetry,[status(thm)],[6551])).
% 1.55/1.78 tff(6553,plain,
% 1.55/1.78 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.55/1.78 inference(transitivity,[status(thm)],[6552, 6550])).
% 1.55/1.78 tff(6554,plain,
% 1.55/1.78 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(z)), s(z)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6553])).
% 1.55/1.78 tff(6555,plain,
% 1.55/1.78 (s(s(elem!1)) = s(s(z))),
% 1.55/1.78 inference(symmetry,[status(thm)],[6417])).
% 1.55/1.78 tff(6556,plain,
% 1.55/1.78 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6555])).
% 1.55/1.78 tff(6557,plain,
% 1.55/1.78 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.55/1.78 inference(symmetry,[status(thm)],[6556])).
% 1.55/1.78 tff(6558,plain,
% 1.55/1.78 (r(s(s(z)), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1814, 6415, 6031])).
% 1.55/1.78 tff(6559,plain,
% 1.55/1.78 (r(s(s(elem!1)), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6558, 6557])).
% 1.55/1.78 tff(6560,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(6561,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(6562,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6561, 6560])).
% 1.55/1.78 tff(6563,plain,
% 1.55/1.78 (~r(s(s(elem!1)), s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6562, 108, 6542, 6521, 6559])).
% 1.55/1.78 tff(6564,plain,
% 1.55/1.78 (~r(s(s(z)), s(z))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6563, 6554])).
% 1.55/1.78 tff(6565,plain,
% 1.55/1.78 (b(s(s(z)), s(z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[50, 6564])).
% 1.55/1.78 tff(6566,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6489, 6565, 6548, 6414, 6104])).
% 1.55/1.78 tff(6567,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6568,plain,
% 1.55/1.78 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6567, 284, 5997])).
% 1.55/1.78 tff(6569,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[386, 6568])).
% 1.55/1.78 tff(6570,plain,
% 1.55/1.78 (~b(s(s(z)), s(s(s(z))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[667, 6569, 5920, 6019])).
% 1.55/1.78 tff(6571,plain,
% 1.55/1.78 (z = elem!1),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[5903, 6570, 5995, 284])).
% 1.55/1.78 tff(6572,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6571])).
% 1.55/1.78 tff(6573,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.55/1.78 inference(symmetry,[status(thm)],[6572])).
% 1.55/1.78 tff(6574,plain,
% 1.55/1.78 (~b(s(s(z)), z)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[5885, 6019, 5920, 284])).
% 1.55/1.78 tff(6575,plain,
% 1.55/1.78 (r(s(s(z)), z)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[374, 6574])).
% 1.55/1.78 tff(6576,plain,
% 1.55/1.78 (r(s(s(z)), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1814, 6571, 6575])).
% 1.55/1.78 tff(6577,plain,
% 1.55/1.78 (elem!1 = z),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1056, 6571])).
% 1.55/1.78 tff(6578,plain,
% 1.55/1.78 (b(s(s(s(z))), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6501, 6577, 6019])).
% 1.55/1.78 tff(6579,plain,
% 1.55/1.78 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[874])).
% 1.55/1.78 tff(6580,plain,
% 1.55/1.78 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 1.55/1.78 inference(symmetry,[status(thm)],[6579])).
% 1.55/1.78 tff(6581,plain,
% 1.55/1.78 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), elem!1))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[6580])).
% 1.55/1.78 tff(6582,plain,
% 1.55/1.78 (~b(s(s(s(z))), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[5996, 6581])).
% 1.55/1.78 tff(6583,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[707, 6582])).
% 1.55/1.78 tff(6584,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6585,plain,
% 1.55/1.78 (~(elem!1 = s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6584, 6578, 5996])).
% 1.55/1.78 tff(6586,plain,
% 1.55/1.78 (~b(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6160, 6569, 5920, 6019])).
% 1.55/1.78 tff(6587,plain,
% 1.55/1.78 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[1628])).
% 1.55/1.78 tff(6588,plain,
% 1.55/1.78 (b(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6197, 6587])).
% 1.55/1.78 tff(6589,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[217, 6588])).
% 1.55/1.78 tff(6590,plain,((~b(elem!1, s(s(s(s(z)))))) | b(z, s(s(s(s(z))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6591,plain,
% 1.55/1.78 (~b(elem!1, s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6590, 6577, 6586])).
% 1.55/1.78 tff(6592,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6228, 6591, 284, 6569, 6585, 6576])).
% 1.55/1.78 tff(6593,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), z)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[6592, 6573])).
% 1.55/1.78 tff(6594,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[5994, 6593])).
% 1.55/1.78 tff(6595,plain,((~b(s(s(s(z))), s(s(z)))) | b(s(s(s(z))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(6596,plain,
% 1.55/1.78 (~b(s(s(s(z))), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6595, 5996])).
% 1.55/1.78 tff(6597,plain,
% 1.55/1.78 (r(s(s(s(z))), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[340, 6596])).
% 1.55/1.78 tff(6598,plain,
% 1.55/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6412, 4303, 5920, 5995])).
% 1.55/1.78 tff(6599,plain,
% 1.55/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1122, 6598])).
% 1.55/1.78 tff(6600,plain,
% 1.55/1.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[2598, 130, 81, 2240])).
% 1.55/1.78 tff(6601,plain,
% 1.55/1.78 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[440, 6600])).
% 1.55/1.78 tff(6602,plain,
% 1.55/1.78 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[2489, 130, 2240, 81])).
% 1.55/1.78 tff(6603,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[462, 6602])).
% 1.55/1.78 tff(6604,plain,
% 1.55/1.78 (~b(s(z), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[3205, 233, 6603, 6601, 2854])).
% 1.55/1.78 tff(6605,plain,
% 1.55/1.78 (r(s(z), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[2414, 6604])).
% 1.55/1.78 tff(6606,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6607,plain,
% 1.55/1.79 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6608,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[6607])).
% 1.55/1.79 tff(6609,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[6608, 6606])).
% 1.55/1.79 tff(6610,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(6611,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[6610, 6609])).
% 1.55/1.79 tff(6612,plain,
% 1.55/1.79 (~r(s(s(s(z))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6611, 108, 492, 2240, 6605])).
% 1.55/1.79 tff(6613,plain,
% 1.55/1.79 (b(s(s(s(z))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1090, 6612])).
% 1.55/1.79 tff(6614,plain,
% 1.55/1.79 (~b(s(s(z)), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3213, 233, 6603, 6601, 2854])).
% 1.55/1.79 tff(6615,plain,
% 1.55/1.79 (r(s(s(z)), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[50, 6614])).
% 1.55/1.79 tff(6616,plain,
% 1.55/1.79 (~b(z, s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3585, 389, 6011, 2854])).
% 1.55/1.79 tff(6617,plain,
% 1.55/1.79 (r(z, s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[128, 6616])).
% 1.55/1.79 tff(6618,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6619,plain,
% 1.55/1.79 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6620,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[6619])).
% 1.55/1.79 tff(6621,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[6620, 6618])).
% 1.55/1.79 tff(6622,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(6623,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[6622, 6621])).
% 1.55/1.79 tff(6624,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6623, 233, 389, 5920, 1930, 1072])).
% 1.55/1.79 tff(6625,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(6626,plain,
% 1.55/1.79 (~b(s(s(s(z))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6625, 389, 6011])).
% 1.55/1.79 tff(6627,plain,
% 1.55/1.79 (r(s(s(s(z))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1090, 6626])).
% 1.55/1.79 tff(6628,plain,
% 1.55/1.79 (~r(s(z), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[309, 6627, 247, 6617])).
% 1.55/1.79 tff(6629,plain,
% 1.55/1.79 (b(s(z), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[260, 6628])).
% 1.55/1.79 tff(6630,plain,
% 1.55/1.79 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3489, 649, 81, 492, 2240, 706])).
% 1.55/1.79 tff(6631,plain,
% 1.55/1.79 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[440, 6630])).
% 1.55/1.79 tff(6632,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6633,plain,
% 1.55/1.79 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6634,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[6633])).
% 1.55/1.79 tff(6635,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.55/1.79 inference(transitivity,[status(thm)],[6634, 6632])).
% 1.55/1.79 tff(6636,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(6637,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[6636, 6635])).
% 1.55/1.79 tff(6638,plain,
% 1.55/1.79 (~b(s(z), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6637, 233, 389, 5920, 649, 6631, 402])).
% 1.55/1.79 tff(6639,plain,
% 1.55/1.79 (r(s(z), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[2414, 6638])).
% 1.55/1.79 tff(6640,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6641,plain,
% 1.55/1.79 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6642,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[6641])).
% 1.55/1.79 tff(6643,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.55/1.79 inference(transitivity,[status(thm)],[6642, 6640])).
% 1.55/1.79 tff(6644,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(6645,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[6644, 6643])).
% 1.55/1.79 tff(6646,plain,
% 1.55/1.79 (~b(s(s(z)), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6645, 233, 389, 5920, 649, 2854, 402])).
% 1.55/1.79 tff(6647,plain,
% 1.55/1.79 (r(s(s(z)), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[50, 6646])).
% 1.55/1.79 tff(6648,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3535, 108, 2240, 92, 6647, 6639])).
% 1.55/1.79 tff(6649,plain,((~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(6650,plain,
% 1.55/1.79 (~b(s(s(z)), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6649, 6627, 2240, 389, 6629, 2854, 81, 492, 5999])).
% 1.55/1.79 tff(6651,plain,
% 1.55/1.79 (r(s(s(z)), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[374, 6650])).
% 1.55/1.79 tff(6652,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6653,plain,
% 1.55/1.79 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6654,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z)))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[6653])).
% 1.55/1.79 tff(6655,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[6654, 6652])).
% 1.55/1.79 tff(6656,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(6657,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(z)))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[6656, 6655])).
% 1.55/1.79 tff(6658,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6657, 108, 6651, 2240, 247, 6617])).
% 1.55/1.79 tff(6659,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(6660,plain,
% 1.55/1.79 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6659, 247, 2240, 2854, 81, 492])).
% 1.55/1.79 tff(6661,plain,
% 1.55/1.79 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[386, 6660])).
% 1.55/1.79 tff(6662,plain,
% 1.55/1.79 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[2598, 6661, 81, 2240])).
% 1.55/1.79 tff(6663,plain,
% 1.55/1.79 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[440, 6662])).
% 1.55/1.79 tff(6664,plain,
% 1.55/1.79 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[2489, 6661, 2240, 81])).
% 1.55/1.79 tff(6665,plain,
% 1.55/1.79 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[462, 6664])).
% 1.55/1.79 tff(6666,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6667,plain,
% 1.55/1.79 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6668,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[6667])).
% 1.55/1.79 tff(6669,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[6668, 6666])).
% 1.55/1.79 tff(6670,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(6671,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[6670, 6669])).
% 1.55/1.79 tff(6672,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6671, 233, 5999, 6665, 6663, 6011])).
% 1.55/1.79 tff(6673,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(6674,plain,
% 1.55/1.79 (~r(s(s(s(z))), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6673, 2240, 81, 2854, 492])).
% 1.55/1.79 tff(6675,plain,
% 1.55/1.79 (b(s(s(s(z))), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[244, 6674])).
% 1.55/1.79 tff(6676,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6677,plain,
% 1.55/1.79 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6678,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[6677])).
% 1.55/1.79 tff(6679,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[6678, 6676])).
% 1.55/1.79 tff(6680,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(6681,plain,
% 1.55/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[6680, 6679])).
% 1.55/1.79 tff(6682,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6681, 233, 272, 1072, 2854, 388])).
% 1.55/1.79 tff(6683,plain,((~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(6684,plain,
% 1.55/1.79 (~b(z, s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6683, 6613, 6675, 2854])).
% 1.55/1.79 tff(6685,plain,
% 1.55/1.79 (r(z, s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[128, 6684])).
% 1.55/1.79 tff(6686,plain,
% 1.55/1.79 (~r(s(s(z)), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3406, 6613, 2854, 2240, 130, 6601])).
% 1.55/1.79 tff(6687,plain,
% 1.55/1.79 (b(s(s(z)), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[374, 6686])).
% 1.55/1.79 tff(6688,plain,
% 1.55/1.79 (~b(s(z), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[6092, 6613, 5920, 6675])).
% 1.55/1.79 tff(6689,plain,
% 1.55/1.79 (r(s(z), z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[260, 6688])).
% 1.55/1.79 tff(6690,plain,
% 1.55/1.79 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3081, 108, 2051, 246, 747])).
% 1.55/1.79 tff(6691,plain,
% 1.55/1.79 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[535, 45, 532, 6690])).
% 1.55/1.79 tff(6692,plain,
% 1.55/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(6693,plain,
% 1.55/1.79 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.80 tff(6694,plain,
% 1.55/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.55/1.80 inference(monotonicity,[status(thm)],[6693])).
% 1.55/1.80 tff(6695,plain,
% 1.55/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.80 inference(transitivity,[status(thm)],[6694, 6692])).
% 1.55/1.80 tff(6696,plain,
% 1.55/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.80 inference(quant_inst,[status(thm)],[])).
% 1.55/1.80 tff(6697,plain,
% 1.55/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.80 inference(modus_ponens,[status(thm)],[6696, 6695])).
% 1.55/1.80 tff(6698,plain,
% 1.55/1.80 ($false),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[6697, 233, 273, 649, 3169, 6691])).
% 1.55/1.80 tff(6699,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.80 tff(6700,plain,
% 1.55/1.80 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[6699, 6689, 5920, 6687, 6685, 6615])).
% 1.55/1.80 tff(6701,plain,
% 1.55/1.80 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[3933, 6700])).
% 1.55/1.80 tff(6702,plain,
% 1.55/1.80 ($false),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[3046, 233, 1547, 1072, 2854, 504])).
% 1.55/1.80 tff(6703,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.80 tff(6704,plain,
% 1.55/1.80 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[6703, 6701, 2854, 6613])).
% 1.55/1.80 tff(6705,plain,
% 1.55/1.80 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[598, 6704])).
% 1.55/1.80 tff(6706,plain,
% 1.55/1.80 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[2316, 108, 492, 2240, 6705])).
% 1.55/1.80 tff(6707,plain,
% 1.55/1.80 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[535, 45, 532, 6706])).
% 1.55/1.80 tff(6708,plain,
% 1.55/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.80 inference(rewrite,[status(thm)],[])).
% 1.55/1.80 tff(6709,plain,
% 1.55/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.80 inference(quant_inst,[status(thm)],[])).
% 1.55/1.80 tff(6710,plain,
% 1.55/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[6709, 6708])).
% 1.65/1.80 tff(6711,plain,
% 1.65/1.80 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6710, 108, 130, 492, 6705])).
% 1.65/1.80 tff(6712,plain,
% 1.65/1.80 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[579, 45, 576, 6711])).
% 1.65/1.80 tff(6713,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6714,plain,
% 1.65/1.80 (((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6715,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[6714])).
% 1.65/1.80 tff(6716,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))))),
% 1.65/1.80 inference(transitivity,[status(thm)],[6715, 6713])).
% 1.65/1.80 tff(6717,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(6718,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[6717, 6716])).
% 1.65/1.80 tff(6719,plain,
% 1.65/1.80 (~r(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6718, 108, 6615, 6685, 6689])).
% 1.65/1.80 tff(6720,plain,
% 1.65/1.80 (b(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[359, 6719])).
% 1.65/1.80 tff(6721,plain,
% 1.65/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6722,plain,
% 1.65/1.80 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6723,plain,
% 1.65/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[6722])).
% 1.65/1.80 tff(6724,plain,
% 1.65/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.80 inference(transitivity,[status(thm)],[6723, 6721])).
% 1.65/1.80 tff(6725,plain,
% 1.65/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(6726,plain,
% 1.65/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[6725, 6724])).
% 1.65/1.80 tff(6727,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6726, 233, 6720, 6687, 6603, 6601, 6712, 6707])).
% 1.65/1.80 tff(6728,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(6729,plain,
% 1.65/1.80 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6728, 4305, 492, 6599, 81])).
% 1.65/1.80 tff(6730,plain,
% 1.65/1.80 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[386, 6729])).
% 1.65/1.80 tff(6731,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3487, 108, 2240, 491, 81, 5995])).
% 1.65/1.80 tff(6732,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(6733,plain,
% 1.65/1.80 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6732, 4305, 81])).
% 1.65/1.80 tff(6734,plain,
% 1.65/1.80 (b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[440, 6733])).
% 1.65/1.80 tff(6735,plain,
% 1.65/1.80 (~b(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3497, 233, 6730, 6734, 6599])).
% 1.65/1.80 tff(6736,plain,
% 1.65/1.80 (r(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2414, 6735])).
% 1.65/1.80 tff(6737,plain,
% 1.65/1.80 (~b(s(s(z)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3505, 233, 6730, 6734, 6599])).
% 1.65/1.80 tff(6738,plain,
% 1.65/1.80 (r(s(s(z)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[50, 6737])).
% 1.65/1.80 tff(6739,plain,
% 1.65/1.80 (~r(s(z), s(s(s(z))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3513, 108, 492, 6738, 6736])).
% 1.65/1.80 tff(6740,plain,
% 1.65/1.80 (b(s(z), s(s(s(z))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[325, 6739])).
% 1.65/1.80 tff(6741,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6742,plain,
% 1.65/1.80 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6743,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[6742])).
% 1.65/1.80 tff(6744,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.65/1.80 inference(transitivity,[status(thm)],[6743, 6741])).
% 1.65/1.80 tff(6745,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(6746,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[6745, 6744])).
% 1.65/1.80 tff(6747,plain,
% 1.65/1.80 (~r(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6746, 108, 492, 6738, 6736])).
% 1.65/1.80 tff(6748,plain,
% 1.65/1.80 (b(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1090, 6747])).
% 1.65/1.80 tff(6749,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3471, 6748, 6740, 6599, 6730])).
% 1.65/1.80 tff(6750,plain,(b(s(s(z)), s(s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(6751,plain,
% 1.65/1.80 (b(s(s(z)), s(s(s(z))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6750, 6597, 5997])).
% 1.65/1.80 tff(6752,plain,
% 1.65/1.80 (~b(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2834, 1072, 5920, 80])).
% 1.65/1.80 tff(6753,plain,
% 1.65/1.80 (r(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[359, 6752])).
% 1.65/1.80 tff(6754,plain,
% 1.65/1.80 (~r(s(s(s(z))), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5476, 6753, 5995, 81])).
% 1.65/1.80 tff(6755,plain,
% 1.65/1.80 (b(s(s(s(z))), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[244, 6754])).
% 1.65/1.80 tff(6756,plain,
% 1.65/1.80 (~b(s(z), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6092, 6755, 5920, 1072])).
% 1.65/1.80 tff(6757,plain,
% 1.65/1.80 (r(s(z), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[260, 6756])).
% 1.65/1.80 tff(6758,plain,
% 1.65/1.80 (~b(s(s(z)), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[657, 6755, 5920, 80])).
% 1.65/1.80 tff(6759,plain,
% 1.65/1.80 (r(s(s(z)), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[374, 6758])).
% 1.65/1.80 tff(6760,plain,
% 1.65/1.80 (~r(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2971, 108, 6759, 6753, 6757])).
% 1.65/1.80 tff(6761,plain,
% 1.65/1.80 (b(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2414, 6760])).
% 1.65/1.80 tff(6762,plain,
% 1.65/1.80 (~r(s(s(z)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2963, 108, 6759, 6753, 6757])).
% 1.65/1.80 tff(6763,plain,
% 1.65/1.80 (b(s(s(z)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[50, 6762])).
% 1.65/1.80 tff(6764,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2986, 6763, 6761, 80, 1072])).
% 1.65/1.80 tff(6765,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(6766,plain,
% 1.65/1.80 (~b(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6765, 6751, 5997])).
% 1.65/1.80 tff(6767,plain,
% 1.65/1.80 (r(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1090, 6766])).
% 1.65/1.80 tff(6768,plain,
% 1.65/1.80 (b(s(s(z)), s(s(s(z))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6750, 492, 81])).
% 1.65/1.80 tff(6769,plain,
% 1.65/1.80 (~b(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6765, 6768, 81])).
% 1.65/1.80 tff(6770,plain,
% 1.65/1.80 (r(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1090, 6769])).
% 1.65/1.80 tff(6771,plain,
% 1.65/1.80 (~r(s(z), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[4152, 6770, 5995, 81])).
% 1.65/1.80 tff(6772,plain,
% 1.65/1.80 (b(s(z), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1122, 6771])).
% 1.65/1.80 tff(6773,plain,
% 1.65/1.80 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2552, 701, 81, 492])).
% 1.65/1.80 tff(6774,plain,
% 1.65/1.80 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[462, 6773])).
% 1.65/1.80 tff(6775,plain,
% 1.65/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6776,plain,
% 1.65/1.80 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6777,plain,
% 1.65/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[6776])).
% 1.65/1.80 tff(6778,plain,
% 1.65/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.80 inference(transitivity,[status(thm)],[6777, 6775])).
% 1.65/1.80 tff(6779,plain,
% 1.65/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(6780,plain,
% 1.65/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[6779, 6778])).
% 1.65/1.80 tff(6781,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6780, 233, 80, 5999, 442, 6011])).
% 1.65/1.80 tff(6782,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(6783,plain,
% 1.65/1.80 (~r(s(s(s(z))), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6782, 6774, 6768, 81])).
% 1.65/1.80 tff(6784,plain,
% 1.65/1.80 (b(s(s(s(z))), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[244, 6783])).
% 1.65/1.80 tff(6785,plain,
% 1.65/1.80 (~b(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[646, 233, 6768, 5920, 6784])).
% 1.65/1.80 tff(6786,plain,
% 1.65/1.80 (r(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[359, 6785])).
% 1.65/1.80 tff(6787,plain,
% 1.65/1.80 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3444, 6786, 5995, 701])).
% 1.65/1.80 tff(6788,plain,
% 1.65/1.80 (b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[440, 6787])).
% 1.65/1.80 tff(6789,plain,
% 1.65/1.80 (~b(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3205, 233, 442, 424, 2854])).
% 1.65/1.80 tff(6790,plain,
% 1.65/1.80 (r(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2414, 6789])).
% 1.65/1.80 tff(6791,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(6792,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(6793,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[6792, 6791])).
% 1.65/1.80 tff(6794,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6793, 108, 492, 92, 51, 6790])).
% 1.65/1.80 tff(6795,plain,(b(s(s(z)), s(z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(6796,plain,
% 1.65/1.80 (b(s(s(z)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6795, 6774, 6770, 492, 6788, 6772])).
% 1.65/1.80 tff(6797,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3213, 233, 6774, 6788, 6772, 6796])).
% 1.65/1.80 tff(6798,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(6799,plain,
% 1.65/1.80 (~r(s(s(z)), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6798, 6597, 5997])).
% 1.65/1.80 tff(6800,plain,
% 1.65/1.80 (b(s(s(z)), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[374, 6799])).
% 1.65/1.80 tff(6801,plain,
% 1.65/1.80 (~b(s(s(s(z))), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[657, 6800, 5920, 6751])).
% 1.65/1.80 tff(6802,plain,
% 1.65/1.80 (r(s(s(s(z))), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[244, 6801])).
% 1.65/1.80 tff(6803,plain,
% 1.65/1.80 (~r(s(z), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[4152, 6767, 5995, 5997])).
% 1.65/1.80 tff(6804,plain,
% 1.65/1.80 (b(s(z), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1122, 6803])).
% 1.65/1.80 tff(6805,plain,
% 1.65/1.80 (~r(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5476, 6802, 5995, 5997])).
% 1.65/1.80 tff(6806,plain,
% 1.65/1.80 (b(z, s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[359, 6805])).
% 1.65/1.80 tff(6807,plain,
% 1.65/1.80 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2845, 6806, 5920, 6751])).
% 1.65/1.80 tff(6808,plain,
% 1.65/1.80 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[759, 6807])).
% 1.65/1.80 tff(6809,plain,
% 1.65/1.80 (~r(z, s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[309, 246, 92, 247])).
% 1.65/1.80 tff(6810,plain,
% 1.65/1.80 (b(z, s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[128, 6809])).
% 1.65/1.80 tff(6811,plain,
% 1.65/1.80 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2892, 246, 92, 2849])).
% 1.65/1.80 tff(6812,plain,
% 1.65/1.80 (b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3933, 6811])).
% 1.65/1.80 tff(6813,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2882, 6812, 6810, 2849, 2854, 247])).
% 1.65/1.80 tff(6814,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6815,plain,
% 1.65/1.81 (~r(s(z), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6814, 6808, 6804, 6802, 6767])).
% 1.65/1.81 tff(6816,plain,
% 1.65/1.81 (b(s(z), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[260, 6815])).
% 1.65/1.81 tff(6817,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6818,plain,
% 1.65/1.81 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6819,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6818])).
% 1.65/1.81 tff(6820,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[6819, 6817])).
% 1.65/1.81 tff(6821,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(6822,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6821, 6820])).
% 1.65/1.81 tff(6823,plain,
% 1.65/1.81 (~b(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6822, 233, 5920, 6800, 6816])).
% 1.65/1.81 tff(6824,plain,
% 1.65/1.81 (r(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2414, 6823])).
% 1.65/1.81 tff(6825,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6826,plain,
% 1.65/1.81 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6827,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6826])).
% 1.65/1.81 tff(6828,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.65/1.81 inference(transitivity,[status(thm)],[6827, 6825])).
% 1.65/1.81 tff(6829,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(6830,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), z))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6829, 6828])).
% 1.65/1.81 tff(6831,plain,
% 1.65/1.81 (~b(s(s(z)), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6830, 233, 5920, 6800, 6816])).
% 1.65/1.81 tff(6832,plain,
% 1.65/1.81 (r(s(s(z)), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[50, 6831])).
% 1.65/1.81 tff(6833,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6793, 108, 6597, 6767, 6832, 6824])).
% 1.65/1.81 tff(6834,plain,(b(s(s(s(z))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6835,plain,
% 1.65/1.81 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3457, 204, 1072, 2854])).
% 1.65/1.81 tff(6836,plain,
% 1.65/1.81 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[386, 6835])).
% 1.65/1.81 tff(6837,plain,
% 1.65/1.81 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3406, 701, 1072, 130, 2854, 4305])).
% 1.65/1.81 tff(6838,plain,
% 1.65/1.81 (r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[440, 6837])).
% 1.65/1.81 tff(6839,plain,
% 1.65/1.81 (~r(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2503, 6838, 4305, 130])).
% 1.65/1.81 tff(6840,plain,
% 1.65/1.81 (b(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[340, 6839])).
% 1.65/1.81 tff(6841,plain,
% 1.65/1.81 (z = elem!1),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5903, 6840, 4303, 3244])).
% 1.65/1.81 tff(6842,plain,
% 1.65/1.81 (s(z) = s(elem!1)),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6841])).
% 1.65/1.81 tff(6843,plain,
% 1.65/1.81 (s(s(z)) = s(s(elem!1))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6842])).
% 1.65/1.81 tff(6844,plain,
% 1.65/1.81 (s(s(elem!1)) = s(s(z))),
% 1.65/1.81 inference(symmetry,[status(thm)],[6843])).
% 1.65/1.81 tff(6845,plain,
% 1.65/1.81 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6844])).
% 1.65/1.81 tff(6846,plain,
% 1.65/1.81 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.65/1.81 inference(symmetry,[status(thm)],[6845])).
% 1.65/1.81 tff(6847,plain,
% 1.65/1.81 (r(s(s(z)), elem!1)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1814, 6841, 701])).
% 1.65/1.81 tff(6848,plain,
% 1.65/1.81 (r(s(s(elem!1)), elem!1)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6847, 6846])).
% 1.65/1.81 tff(6849,plain,
% 1.65/1.81 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6843])).
% 1.65/1.81 tff(6850,plain,
% 1.65/1.81 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6849])).
% 1.65/1.81 tff(6851,plain,
% 1.65/1.81 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.65/1.81 inference(symmetry,[status(thm)],[6850])).
% 1.65/1.81 tff(6852,plain,
% 1.65/1.81 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6851])).
% 1.65/1.81 tff(6853,plain,
% 1.65/1.81 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.65/1.81 inference(symmetry,[status(thm)],[6852])).
% 1.65/1.81 tff(6854,plain,
% 1.65/1.81 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6841])).
% 1.65/1.81 tff(6855,plain,
% 1.65/1.81 (r(s(s(s(s(z)))), elem!1)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[3244, 6854])).
% 1.65/1.81 tff(6856,plain,
% 1.65/1.81 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6855, 6853])).
% 1.65/1.81 tff(6857,plain,
% 1.65/1.81 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6851])).
% 1.65/1.81 tff(6858,plain,
% 1.65/1.81 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.65/1.81 inference(symmetry,[status(thm)],[6857])).
% 1.65/1.81 tff(6859,plain,
% 1.65/1.81 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6843])).
% 1.65/1.81 tff(6860,plain,
% 1.65/1.81 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6838, 6859])).
% 1.65/1.81 tff(6861,plain,
% 1.65/1.81 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6860, 6858])).
% 1.65/1.81 tff(6862,plain,
% 1.65/1.81 (~r(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[4008, 4304, 491, 3244])).
% 1.65/1.81 tff(6863,plain,
% 1.65/1.81 (b(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[222, 6862])).
% 1.65/1.81 tff(6864,plain,
% 1.65/1.81 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3585, 388, 2854, 6863])).
% 1.65/1.81 tff(6865,plain,
% 1.65/1.81 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[386, 6864])).
% 1.65/1.81 tff(6866,plain,
% 1.65/1.81 (~r(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2503, 6865, 4305, 491])).
% 1.65/1.81 tff(6867,plain,
% 1.65/1.81 (b(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[340, 6866])).
% 1.65/1.81 tff(6868,plain,
% 1.65/1.81 (z = elem!1),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5872, 6867, 4303, 3244, 368])).
% 1.65/1.81 tff(6869,plain,
% 1.65/1.81 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2912, 6868, 2854])).
% 1.65/1.81 tff(6870,plain,
% 1.65/1.81 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[1726, 1723])).
% 1.65/1.81 tff(6871,plain,
% 1.65/1.81 (b(s(s(s(elem!1))), s(elem!1))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[1072, 6870])).
% 1.65/1.81 tff(6872,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1603, 6871])).
% 1.65/1.81 tff(6873,plain,((~b(s(s(s(z))), s(z))) | b(s(s(s(elem!1))), s(elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6874,plain,
% 1.65/1.81 (b(s(s(s(elem!1))), s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6873, 6868, 1072])).
% 1.65/1.81 tff(6875,plain,
% 1.65/1.81 (s(z) = s(elem!1)),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6868])).
% 1.65/1.81 tff(6876,plain,
% 1.65/1.81 (s(s(z)) = s(s(elem!1))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6875])).
% 1.65/1.81 tff(6877,plain,
% 1.65/1.81 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6876])).
% 1.65/1.81 tff(6878,plain,
% 1.65/1.81 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.65/1.81 inference(symmetry,[status(thm)],[6877])).
% 1.65/1.81 tff(6879,plain,
% 1.65/1.81 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6878])).
% 1.65/1.81 tff(6880,plain,
% 1.65/1.81 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.65/1.81 inference(symmetry,[status(thm)],[6879])).
% 1.65/1.81 tff(6881,plain,
% 1.65/1.81 (~r(s(s(s(z))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2586, 6865, 4305, 491])).
% 1.65/1.81 tff(6882,plain,
% 1.65/1.81 (b(s(s(s(z))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[244, 6881])).
% 1.65/1.81 tff(6883,plain,
% 1.65/1.81 (elem!1 = z),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1056, 6868])).
% 1.65/1.81 tff(6884,plain,
% 1.65/1.81 (b(s(s(s(z))), elem!1)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6501, 6883, 6882])).
% 1.65/1.81 tff(6885,plain,
% 1.65/1.81 (b(s(s(s(elem!1))), elem!1)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6884, 6880])).
% 1.65/1.81 tff(6886,plain,
% 1.65/1.81 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6877])).
% 1.65/1.81 tff(6887,plain,
% 1.65/1.81 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.65/1.81 inference(symmetry,[status(thm)],[6886])).
% 1.65/1.81 tff(6888,plain,
% 1.65/1.81 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6887])).
% 1.65/1.81 tff(6889,plain,
% 1.65/1.81 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.65/1.81 inference(symmetry,[status(thm)],[6888])).
% 1.65/1.81 tff(6890,plain,
% 1.65/1.81 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6868])).
% 1.65/1.81 tff(6891,plain,
% 1.65/1.81 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6863, 6890])).
% 1.65/1.81 tff(6892,plain,
% 1.65/1.81 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6891, 6889])).
% 1.65/1.81 tff(6893,plain,
% 1.65/1.81 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6877])).
% 1.65/1.81 tff(6894,plain,
% 1.65/1.81 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2598, 6865, 4305, 491])).
% 1.65/1.81 tff(6895,plain,
% 1.65/1.81 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[186, 6894])).
% 1.65/1.81 tff(6896,plain,
% 1.65/1.81 (~r(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3444, 4304, 491, 3244])).
% 1.65/1.81 tff(6897,plain,
% 1.65/1.81 (b(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[359, 6896])).
% 1.65/1.81 tff(6898,plain,
% 1.65/1.81 (~r(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3433, 6882, 6897, 6865, 6895])).
% 1.65/1.81 tff(6899,plain,
% 1.65/1.81 (b(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[78, 6898])).
% 1.65/1.81 tff(6900,plain,
% 1.65/1.81 (b(elem!1, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1746, 6883, 6899])).
% 1.65/1.81 tff(6901,plain,
% 1.65/1.81 (b(elem!1, s(s(s(elem!1))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6900, 6893])).
% 1.65/1.81 tff(6902,plain,
% 1.65/1.81 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6875])).
% 1.65/1.81 tff(6903,plain,
% 1.65/1.81 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6868])).
% 1.65/1.81 tff(6904,plain,
% 1.65/1.81 (b(elem!1, s(z))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[388, 6903])).
% 1.65/1.81 tff(6905,plain,
% 1.65/1.81 (b(elem!1, s(elem!1))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6904, 6902])).
% 1.65/1.81 tff(6906,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6907,plain,
% 1.65/1.81 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6908,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6907])).
% 1.65/1.81 tff(6909,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.65/1.81 inference(transitivity,[status(thm)],[6908, 6906])).
% 1.65/1.81 tff(6910,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(6911,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6910, 6909])).
% 1.65/1.81 tff(6912,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6911, 233, 6905, 6901, 6892, 6885, 6874, 6869])).
% 1.65/1.81 tff(6913,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | b(s(s(z)), s(s(s(z)))) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), z) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6914,plain,
% 1.65/1.81 (~b(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6913, 368, 1072, 4303, 3244, 2854, 491])).
% 1.65/1.81 tff(6915,plain,
% 1.65/1.81 (r(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[128, 6914])).
% 1.65/1.81 tff(6916,plain,
% 1.65/1.81 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[1053])).
% 1.65/1.81 tff(6917,plain,
% 1.65/1.81 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.65/1.81 inference(symmetry,[status(thm)],[6916])).
% 1.65/1.81 tff(6918,plain,
% 1.65/1.81 ((~r(elem!1, s(z))) <=> (~r(z, s(z)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6917])).
% 1.65/1.81 tff(6919,plain,
% 1.65/1.81 (~r(z, s(z))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[1357, 6918])).
% 1.65/1.81 tff(6920,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[98, 6919])).
% 1.65/1.81 tff(6921,plain,((~(z = elem!1)) | (~r(z, s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6922,plain,
% 1.65/1.81 (~(z = elem!1)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6921, 6915, 1357])).
% 1.65/1.81 tff(6923,plain,
% 1.65/1.81 (~b(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5903, 6922, 4303, 3244])).
% 1.65/1.81 tff(6924,plain,
% 1.65/1.81 (r(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[340, 6923])).
% 1.65/1.81 tff(6925,plain,
% 1.65/1.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2503, 6924, 4305, 491])).
% 1.65/1.81 tff(6926,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[386, 6925])).
% 1.65/1.81 tff(6927,plain,
% 1.65/1.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3457, 6926, 1072, 2854])).
% 1.65/1.81 tff(6928,plain,
% 1.65/1.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[186, 6927])).
% 1.65/1.81 tff(6929,plain,
% 1.65/1.81 (~r(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2612, 6928, 4305, 4304])).
% 1.65/1.81 tff(6930,plain,
% 1.65/1.81 (b(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[78, 6929])).
% 1.65/1.81 tff(6931,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6623, 233, 6926, 6930, 6863, 1072])).
% 1.65/1.81 tff(6932,plain,(b(s(s(z)), z) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z)))) | (~r(s(s(s(s(z)))), z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6933,plain,
% 1.65/1.81 (b(s(s(z)), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6932, 3244, 2854, 491, 4303, 1072, 1357])).
% 1.65/1.81 tff(6934,plain,
% 1.65/1.81 (~r(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3326, 284, 649, 3244, 2240])).
% 1.65/1.81 tff(6935,plain,
% 1.65/1.81 (b(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[78, 6934])).
% 1.65/1.81 tff(6936,plain,
% 1.65/1.81 (~b(s(s(s(z))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5885, 6935, 649, 284])).
% 1.65/1.81 tff(6937,plain,
% 1.65/1.81 (r(s(s(s(z))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[244, 6936])).
% 1.65/1.81 tff(6938,plain,
% 1.65/1.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2586, 6937, 2240, 491])).
% 1.65/1.81 tff(6939,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[386, 6938])).
% 1.65/1.81 tff(6940,plain,
% 1.65/1.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3457, 6939, 1072, 2854])).
% 1.65/1.81 tff(6941,plain,
% 1.65/1.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[186, 6940])).
% 1.65/1.81 tff(6942,plain,
% 1.65/1.81 (~b(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5448, 6939, 284, 6935])).
% 1.65/1.81 tff(6943,plain,
% 1.65/1.81 (r(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[222, 6942])).
% 1.65/1.81 tff(6944,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6009, 6943, 6941, 3244, 6937])).
% 1.65/1.81 tff(6945,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6946,plain,
% 1.65/1.81 (~b(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6945, 3244, 1072, 2854, 4305, 491, 6933])).
% 1.65/1.81 tff(6947,plain,
% 1.65/1.81 (r(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[340, 6946])).
% 1.65/1.81 tff(6948,plain,
% 1.65/1.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2503, 6947, 4305, 491])).
% 1.65/1.81 tff(6949,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[386, 6948])).
% 1.65/1.81 tff(6950,plain,
% 1.65/1.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3457, 6949, 1072, 2854])).
% 1.65/1.81 tff(6951,plain,
% 1.65/1.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[186, 6950])).
% 1.65/1.81 tff(6952,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3487, 108, 4305, 491, 6951, 3244])).
% 1.65/1.81 tff(6953,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z)))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6954,plain,
% 1.65/1.81 (~r(s(s(s(s(z)))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6953, 491, 1072, 2854, 4303, 1357])).
% 1.65/1.81 tff(6955,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3228, 6954])).
% 1.65/1.81 tff(6956,plain,
% 1.65/1.81 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3241, 6955, 2854, 1072])).
% 1.65/1.81 tff(6957,plain,
% 1.65/1.81 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[186, 6956])).
% 1.65/1.81 tff(6958,plain,
% 1.65/1.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2598, 6957, 4305, 491])).
% 1.65/1.81 tff(6959,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[386, 6958])).
% 1.65/1.81 tff(6960,plain,
% 1.65/1.81 (~b(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2530, 6959, 6955, 1072])).
% 1.65/1.81 tff(6961,plain,
% 1.65/1.81 (r(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[78, 6960])).
% 1.65/1.81 tff(6962,plain,
% 1.65/1.81 (~r(s(s(z)), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2612, 6961, 4305, 6957])).
% 1.65/1.81 tff(6963,plain,
% 1.65/1.81 (b(s(s(z)), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[374, 6962])).
% 1.65/1.81 tff(6964,plain,
% 1.65/1.81 (~r(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2475, 108, 4305, 6961, 6957])).
% 1.65/1.81 tff(6965,plain,
% 1.65/1.81 (b(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[359, 6964])).
% 1.65/1.81 tff(6966,plain,
% 1.65/1.81 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2256, 233, 6965, 6963, 6955])).
% 1.65/1.81 tff(6967,plain,
% 1.65/1.81 (r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[462, 6966])).
% 1.65/1.81 tff(6968,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2465, 108, 4305, 6967, 491, 6957])).
% 1.65/1.81 tff(6969,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z)))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(6970,plain,
% 1.65/1.81 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6969, 1357, 2854, 4303, 1072])).
% 1.65/1.81 tff(6971,plain,
% 1.65/1.81 (b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[440, 6970])).
% 1.65/1.81 tff(6972,plain,
% 1.65/1.81 (~r(s(s(z)), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3406, 4307, 1072, 6971, 2854, 4305])).
% 1.65/1.81 tff(6973,plain,
% 1.65/1.81 (b(s(s(z)), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[374, 6972])).
% 1.65/1.81 tff(6974,plain,
% 1.65/1.81 (~r(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3338, 4307, 6973, 4305, 2854, 1072])).
% 1.65/1.81 tff(6975,plain,
% 1.65/1.81 (b(z, s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[78, 6974])).
% 1.65/1.81 tff(6976,plain,
% 1.65/1.81 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2489, 5997, 4305, 4307])).
% 1.65/1.81 tff(6977,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[462, 6976])).
% 1.65/1.81 tff(6978,plain,
% 1.65/1.81 (~b(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3205, 233, 6977, 6971, 2854])).
% 1.65/1.81 tff(6979,plain,
% 1.65/1.81 (r(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[481, 45, 34, 6978])).
% 1.65/1.81 tff(6980,plain,
% 1.65/1.81 (~r(s(z), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[4285, 108, 3699, 4305, 6979])).
% 1.65/1.81 tff(6981,plain,
% 1.65/1.81 (b(s(z), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[325, 6980])).
% 1.65/1.81 tff(6982,plain,
% 1.65/1.81 (~b(s(z), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2195, 233, 6975, 1072, 6981])).
% 1.65/1.81 tff(6983,plain,
% 1.65/1.81 (r(s(z), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[260, 6982])).
% 1.65/1.81 tff(6984,plain,
% 1.65/1.81 (~b(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2203, 233, 6975, 1072, 6981])).
% 1.65/1.81 tff(6985,plain,
% 1.65/1.81 (r(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[128, 6984])).
% 1.65/1.81 tff(6986,plain,
% 1.65/1.81 (~b(s(s(z)), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3213, 233, 6977, 6971, 2854])).
% 1.65/1.81 tff(6987,plain,
% 1.65/1.81 (r(s(s(z)), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[48, 45, 35, 6986])).
% 1.65/1.81 tff(6988,plain,
% 1.65/1.81 (~r(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6718, 108, 6987, 6985, 6983])).
% 1.65/1.81 tff(6989,plain,
% 1.65/1.81 (b(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[359, 6988])).
% 1.65/1.81 tff(6990,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6991,plain,
% 1.65/1.81 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(6992,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[6991])).
% 1.65/1.81 tff(6993,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.81 inference(transitivity,[status(thm)],[6992, 6990])).
% 1.65/1.81 tff(6994,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(6995,plain,
% 1.65/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[6994, 6993])).
% 1.65/1.81 tff(6996,plain,
% 1.65/1.81 (~b(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6995, 233, 6989, 6973, 6977])).
% 1.65/1.81 tff(6997,plain,
% 1.65/1.81 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6699, 6985, 6973, 6975, 6983, 6987])).
% 1.65/1.81 tff(6998,plain,
% 1.65/1.81 (~(z = elem!1)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6921, 6985, 1357])).
% 1.65/1.81 tff(6999,plain,
% 1.65/1.81 (~b(s(s(s(s(z)))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[677, 6977, 6973, 6975])).
% 1.65/1.81 tff(7000,plain,
% 1.65/1.81 (r(s(s(s(s(z)))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3228, 6999])).
% 1.65/1.81 tff(7001,plain,
% 1.65/1.81 (r(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[222, 6996])).
% 1.65/1.81 tff(7002,plain,
% 1.65/1.81 (~r(s(s(s(z))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[6009, 7001, 7000, 5997])).
% 1.65/1.81 tff(7003,plain,
% 1.65/1.81 (b(s(s(s(z))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[244, 7002])).
% 1.65/1.81 tff(7004,plain,
% 1.65/1.81 (b(elem!1, z)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[272, 5211])).
% 1.65/1.81 tff(7005,plain,
% 1.65/1.81 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[834])).
% 1.65/1.81 tff(7006,plain,
% 1.65/1.81 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.65/1.81 inference(symmetry,[status(thm)],[7005])).
% 1.65/1.81 tff(7007,assumption,(elem!1 = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.65/1.81 tff(7008,plain,
% 1.65/1.81 (s(s(s(s(s(z))))) = elem!1),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[7007, 1254])).
% 1.65/1.81 tff(7009,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.65/1.81 tff(7010,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[7009, 7008])).
% 1.65/1.81 tff(7011,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(7012,plain,
% 1.65/1.81 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[7011, 1271])).
% 1.65/1.81 tff(7013,plain,
% 1.65/1.81 (b(z, elem!1)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1030, 834, 273])).
% 1.65/1.81 tff(7014,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.65/1.81 tff(7015,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(7016,plain,
% 1.65/1.81 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(7017,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[7016])).
% 1.65/1.81 tff(7018,plain,
% 1.65/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7017, 7015])).
% 1.65/1.82 tff(7019,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7020,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7019, 7018])).
% 1.65/1.82 tff(7021,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7020, 233, 921, 809, 1290, 7014])).
% 1.65/1.82 tff(7022,plain,((~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(7023,plain,
% 1.65/1.82 (~b(s(s(elem!1)), z)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7022, 1290, 809, 921])).
% 1.65/1.82 tff(7024,plain,
% 1.65/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7025,plain,
% 1.65/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7026,plain,
% 1.65/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7025, 7024])).
% 1.65/1.82 tff(7027,plain,
% 1.65/1.82 (r(s(s(elem!1)), z)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7026, 45, 1434, 7023])).
% 1.65/1.82 tff(7028,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7029,plain,
% 1.65/1.82 (((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7030,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7029])).
% 1.65/1.82 tff(7031,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7030, 7028])).
% 1.65/1.82 tff(7032,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7033,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7032, 7031])).
% 1.65/1.82 tff(7034,plain,
% 1.65/1.82 (~r(s(z), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7033, 108, 98, 246, 7027])).
% 1.65/1.82 tff(7035,plain,
% 1.65/1.82 (b(s(z), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1352, 7034])).
% 1.65/1.82 tff(7036,plain,
% 1.65/1.82 (~b(s(s(elem!1)), s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5231, 7035, 967, 1290])).
% 1.65/1.82 tff(7037,plain,
% 1.65/1.82 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1417, 7036, 834])).
% 1.65/1.82 tff(7038,plain,
% 1.65/1.82 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1409, 7037, 5707])).
% 1.65/1.82 tff(7039,plain,
% 1.65/1.82 (r(s(s(elem!1)), s(elem!1))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7038, 1399])).
% 1.65/1.82 tff(7040,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7041,plain,
% 1.65/1.82 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7042,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7041])).
% 1.65/1.82 tff(7043,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7042, 7040])).
% 1.65/1.82 tff(7044,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7045,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7044, 7043])).
% 1.65/1.82 tff(7046,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7045, 233, 1290, 967, 1328, 5775])).
% 1.65/1.82 tff(7047,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(7048,plain,
% 1.65/1.82 (~b(s(s(elem!1)), elem!1)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7047, 7035, 967, 1290])).
% 1.65/1.82 tff(7049,plain,
% 1.65/1.82 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1551, 7048, 834])).
% 1.65/1.82 tff(7050,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[598, 7049])).
% 1.65/1.82 tff(7051,plain,
% 1.65/1.82 (r(s(s(elem!1)), elem!1)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1541, 7050, 834])).
% 1.65/1.82 tff(7052,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7053,plain,
% 1.65/1.82 (((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7054,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7053])).
% 1.65/1.82 tff(7055,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7054, 7052])).
% 1.65/1.82 tff(7056,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7057,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7056, 7055])).
% 1.65/1.82 tff(7058,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7057, 108, 994, 5153, 7051, 7039])).
% 1.65/1.82 tff(7059,plain,((~b(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(7060,plain,
% 1.65/1.82 (~b(elem!1, s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7059, 4431, 5144, 834, 4921, 2205, 2197, 7004, 7013])).
% 1.65/1.82 tff(7061,plain,
% 1.65/1.82 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5690, 7060, 834])).
% 1.65/1.82 tff(7062,plain,
% 1.65/1.82 (r(elem!1, s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5685, 7061, 7012])).
% 1.65/1.82 tff(7063,plain,
% 1.65/1.82 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7062, 7006])).
% 1.65/1.82 tff(7064,plain,
% 1.65/1.82 (b(s(s(z)), s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5596, 834, 424])).
% 1.65/1.82 tff(7065,plain,
% 1.65/1.82 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[1257])).
% 1.65/1.82 tff(7066,plain,
% 1.65/1.82 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.65/1.82 inference(symmetry,[status(thm)],[7065])).
% 1.65/1.82 tff(7067,plain,
% 1.65/1.82 ((~r(s(s(z)), s(s(s(s(s(z))))))) <=> (~r(s(s(z)), s(s(elem!1))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7066])).
% 1.65/1.82 tff(7068,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7069,plain,
% 1.65/1.82 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7070,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7069])).
% 1.65/1.82 tff(7071,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7070, 7068])).
% 1.65/1.82 tff(7072,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7073,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7072, 7071])).
% 1.65/1.82 tff(7074,plain,
% 1.65/1.82 ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7073, 108])).
% 1.65/1.82 tff(7075,plain,
% 1.65/1.82 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7074, 1537, 2240, 81])).
% 1.65/1.82 tff(7076,plain,
% 1.65/1.82 (~r(s(s(z)), s(s(elem!1)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7075, 7067])).
% 1.65/1.82 tff(7077,plain,
% 1.65/1.82 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[1257])).
% 1.65/1.82 tff(7078,plain,
% 1.65/1.82 ((s(s(z)) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7077, 4093])).
% 1.65/1.82 tff(7079,plain,
% 1.65/1.82 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.65/1.82 inference(symmetry,[status(thm)],[7078])).
% 1.65/1.82 tff(7080,plain,
% 1.65/1.82 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7079])).
% 1.65/1.82 tff(7081,plain,
% 1.65/1.82 (~(s(s(z)) = s(s(elem!1)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[532, 7080])).
% 1.65/1.82 tff(7082,plain,
% 1.65/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7083,plain,
% 1.65/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7084,plain,
% 1.65/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7083, 7082])).
% 1.65/1.82 tff(7085,plain,
% 1.65/1.82 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7084, 45])).
% 1.65/1.82 tff(7086,plain,
% 1.65/1.82 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7085, 7081, 7076])).
% 1.65/1.82 tff(7087,plain,
% 1.65/1.82 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[1399])).
% 1.65/1.82 tff(7088,plain,
% 1.65/1.82 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7087])).
% 1.65/1.82 tff(7089,plain,
% 1.65/1.82 (r(s(s(elem!1)), elem!1)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1541, 1537, 834])).
% 1.65/1.82 tff(7090,plain,
% 1.65/1.82 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7057, 108, 994, 5153, 7089])).
% 1.65/1.82 tff(7091,plain,
% 1.65/1.82 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7090, 7088])).
% 1.65/1.82 tff(7092,plain,
% 1.65/1.82 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1409, 7091, 5707])).
% 1.65/1.82 tff(7093,plain,
% 1.65/1.82 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1417, 7092, 834])).
% 1.65/1.82 tff(7094,plain,
% 1.65/1.82 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[3064, 1537, 130, 2849])).
% 1.65/1.82 tff(7095,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[745, 7094])).
% 1.65/1.82 tff(7096,plain,
% 1.65/1.82 (b(s(elem!1), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1277, 7095, 834])).
% 1.65/1.82 tff(7097,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7098,plain,
% 1.65/1.82 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7099,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7098])).
% 1.65/1.82 tff(7100,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7099, 7097])).
% 1.65/1.82 tff(7101,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7102,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7101, 7100])).
% 1.65/1.82 tff(7103,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7102, 233, 7096, 7093, 5604, 7086])).
% 1.65/1.82 tff(7104,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(elem!1))) | (~(s(s(s(z))) = elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(7105,plain,
% 1.65/1.82 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7104, 7064, 834, 4431, 5144, 4307, 7063, 2240, 81])).
% 1.65/1.82 tff(7106,plain,
% 1.65/1.82 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[598, 7105])).
% 1.65/1.82 tff(7107,plain,
% 1.65/1.82 (b(s(s(elem!1)), elem!1)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1551, 7106, 834])).
% 1.65/1.82 tff(7108,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7109,plain,
% 1.65/1.82 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7110,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7109])).
% 1.65/1.82 tff(7111,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7110, 7108])).
% 1.65/1.82 tff(7112,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7113,plain,
% 1.65/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7112, 7111])).
% 1.65/1.82 tff(7114,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7113, 233, 809, 1102, 1288, 5775])).
% 1.65/1.82 tff(7115,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(7116,plain,
% 1.65/1.82 (~b(s(s(elem!1)), s(z))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7115, 7107, 7004, 1478])).
% 1.65/1.82 tff(7117,plain,
% 1.65/1.82 (~b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1283, 7116, 834])).
% 1.65/1.82 tff(7118,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[556, 7117, 5188])).
% 1.65/1.82 tff(7119,plain,
% 1.65/1.82 (r(s(s(elem!1)), s(z))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7118, 1476])).
% 1.65/1.82 tff(7120,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7121,plain,
% 1.65/1.82 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7122,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[7121])).
% 1.65/1.82 tff(7123,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[7122, 7120])).
% 1.65/1.82 tff(7124,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(7125,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7124, 7123])).
% 1.65/1.82 tff(7126,plain,
% 1.65/1.82 (~r(s(s(elem!1)), z)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7125, 108, 2205, 2197, 7119])).
% 1.65/1.82 tff(7127,plain,
% 1.65/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7128,plain,
% 1.65/1.82 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(7129,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7128])).
% 1.65/1.83 tff(7130,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7129, 7127])).
% 1.65/1.83 tff(7131,plain,
% 1.65/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(7132,plain,
% 1.65/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[7131, 7130])).
% 1.65/1.83 tff(7133,plain,
% 1.65/1.83 (~b(s(s(elem!1)), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7132, 233, 7013, 7004, 7107])).
% 1.65/1.83 tff(7134,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7026, 45, 1434, 7133, 7126])).
% 1.65/1.83 tff(7135,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(7136,plain,
% 1.65/1.83 (~(s(s(s(z))) = elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7135, 6981, 5997, 4305, 1072, 7003, 3699, 4306, 6971, 6975])).
% 1.65/1.83 tff(7137,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7138,plain,
% 1.65/1.83 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7139,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7138])).
% 1.65/1.83 tff(7140,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7139, 7137])).
% 1.65/1.83 tff(7141,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(7142,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[7141, 7140])).
% 1.65/1.83 tff(7143,plain,
% 1.65/1.83 (~r(s(s(s(s(z)))), s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7142, 108, 7001, 7000, 6983])).
% 1.65/1.83 tff(7144,plain,
% 1.65/1.83 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[200, 45, 7143])).
% 1.65/1.83 tff(7145,plain,
% 1.65/1.83 (b(s(s(s(s(z)))), s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7144, 96])).
% 1.65/1.83 tff(7146,plain,
% 1.65/1.83 (r(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[481, 45, 34, 6789])).
% 1.65/1.83 tff(7147,plain,
% 1.65/1.83 (~r(s(z), s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[4285, 108, 3699, 4305, 7146])).
% 1.65/1.83 tff(7148,plain,
% 1.65/1.83 (~b(s(s(s(s(z)))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[677, 442, 649, 273])).
% 1.65/1.83 tff(7149,plain,
% 1.65/1.83 (~b(s(s(s(z))), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[4992, 809, 273, 272])).
% 1.65/1.83 tff(7150,plain,
% 1.65/1.83 (r(elem!1, s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[886, 4764, 873])).
% 1.65/1.83 tff(7151,plain,
% 1.65/1.83 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[943])).
% 1.65/1.83 tff(7152,plain,
% 1.65/1.83 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.65/1.83 inference(symmetry,[status(thm)],[7151])).
% 1.65/1.83 tff(7153,plain,
% 1.65/1.83 (r(s(z), s(s(s(z))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[888, 7152])).
% 1.65/1.83 tff(7154,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[314, 7153])).
% 1.65/1.83 tff(7155,plain,((~(s(z) = elem!1)) | r(s(z), s(s(s(z)))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(7156,plain,
% 1.65/1.83 (~(s(z) = elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7155, 7150, 314])).
% 1.65/1.83 tff(7157,plain,
% 1.65/1.83 (~(elem!1 = s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[956, 7156])).
% 1.65/1.83 tff(7158,plain,
% 1.65/1.83 (b(elem!1, s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[965, 7157, 1357])).
% 1.65/1.83 tff(7159,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7160,plain,
% 1.65/1.83 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7161,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7160])).
% 1.65/1.83 tff(7162,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7161, 7159])).
% 1.65/1.83 tff(7163,plain,
% 1.65/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(7164,plain,
% 1.65/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 1.65/1.83 tff(7165,plain,
% 1.65/1.83 (~b(elem!1, s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7164, 233, 442, 424, 7158, 2854, 203])).
% 1.65/1.83 tff(7166,plain,
% 1.65/1.83 (r(s(s(s(z))), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[843, 1049, 797])).
% 1.65/1.83 tff(7167,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7168,plain,
% 1.65/1.83 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7169,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7168])).
% 1.65/1.83 tff(7170,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7169, 7167])).
% 1.65/1.83 tff(7171,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(7172,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[7171, 7170])).
% 1.65/1.83 tff(7173,plain,
% 1.65/1.83 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7172, 108, 4307, 7166, 7150])).
% 1.65/1.83 tff(7174,plain,
% 1.65/1.83 (elem!1 = s(s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[850, 7173, 7165])).
% 1.65/1.83 tff(7175,plain,
% 1.65/1.83 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.65/1.83 inference(monotonicity,[status(thm)],[6230])).
% 1.65/1.83 tff(7176,plain,
% 1.65/1.83 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.65/1.83 inference(symmetry,[status(thm)],[7175])).
% 1.65/1.83 tff(7177,plain,
% 1.65/1.83 (b(z, s(s(s(s(z)))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[921, 7176])).
% 1.65/1.83 tff(7178,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[217, 7177])).
% 1.65/1.83 tff(7179,plain,(b(z, s(s(s(s(z))))) | (~b(z, elem!1)) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(7180,plain,
% 1.65/1.83 (~b(z, elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7179, 7174, 217])).
% 1.65/1.83 tff(7181,plain,
% 1.65/1.83 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7174])).
% 1.65/1.83 tff(7182,plain,
% 1.65/1.83 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 1.65/1.83 inference(symmetry,[status(thm)],[7181])).
% 1.65/1.83 tff(7183,plain,
% 1.65/1.83 ((~b(s(s(s(s(z)))), z)) <=> (~b(elem!1, z))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7182])).
% 1.65/1.83 tff(7184,plain,
% 1.65/1.83 (~b(elem!1, z)),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[3226, 7183])).
% 1.65/1.83 tff(7185,plain,
% 1.65/1.83 ((elem!1 = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7174])).
% 1.65/1.83 tff(7186,plain,
% 1.65/1.83 ((elem!1 = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7185, 143])).
% 1.65/1.83 tff(7187,plain,
% 1.65/1.83 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(z)))),
% 1.65/1.83 inference(symmetry,[status(thm)],[7186])).
% 1.65/1.83 tff(7188,plain,
% 1.65/1.83 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 1.65/1.83 inference(transitivity,[status(thm)],[7187, 1004])).
% 1.65/1.83 tff(7189,plain,
% 1.65/1.83 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7188])).
% 1.65/1.83 tff(7190,plain,
% 1.65/1.83 (~(s(s(z)) = elem!1)),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[169, 7189])).
% 1.65/1.83 tff(7191,plain,
% 1.65/1.83 (~(s(s(s(z))) = elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1030, 273, 1027])).
% 1.65/1.83 tff(7192,plain,
% 1.65/1.83 (~(elem!1 = s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1051, 7191])).
% 1.65/1.83 tff(7193,plain,
% 1.65/1.83 (~r(s(s(z)), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1218, 4555, 862, 3699])).
% 1.65/1.83 tff(7194,plain,
% 1.65/1.83 (b(s(s(z)), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1175, 7193, 1212])).
% 1.65/1.83 tff(7195,plain,
% 1.65/1.83 (r(z, elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[934, 717, 1027])).
% 1.65/1.83 tff(7196,plain,
% 1.65/1.83 (~r(s(s(s(z))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1042, 108, 7195, 4555, 862])).
% 1.65/1.83 tff(7197,plain,
% 1.65/1.83 (b(s(s(s(z))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[244, 7196])).
% 1.65/1.83 tff(7198,plain,
% 1.65/1.83 (~r(elem!1, s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[4747, 701, 938, 1059])).
% 1.65/1.83 tff(7199,plain,
% 1.65/1.83 (b(elem!1, s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1236, 7198, 4505])).
% 1.65/1.83 tff(7200,plain,
% 1.65/1.83 (~r(s(s(s(z))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1042, 108, 938, 1059, 862])).
% 1.65/1.83 tff(7201,plain,
% 1.65/1.83 (b(s(s(s(z))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[244, 7200])).
% 1.65/1.83 tff(7202,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7203,plain,
% 1.65/1.83 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7204,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7203])).
% 1.65/1.83 tff(7205,plain,
% 1.65/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7204, 7202])).
% 1.65/1.83 tff(7206,plain,
% 1.65/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(7207,plain,
% 1.65/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[7206, 7205])).
% 1.65/1.83 tff(7208,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7207, 233, 920, 919, 80, 272])).
% 1.65/1.83 tff(7209,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(7210,plain,
% 1.65/1.83 (~b(s(s(z)), s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7209, 919, 920, 7201])).
% 1.65/1.83 tff(7211,plain,
% 1.65/1.83 (r(s(s(z)), s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[2228, 7210])).
% 1.65/1.83 tff(7212,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7213,plain,
% 1.65/1.83 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7214,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7213])).
% 1.65/1.83 tff(7215,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7214, 7212])).
% 1.65/1.83 tff(7216,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(7217,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[7216, 7215])).
% 1.65/1.83 tff(7218,plain,
% 1.65/1.83 (~r(s(z), s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7217, 108, 130, 862, 2337])).
% 1.65/1.83 tff(7219,plain,
% 1.65/1.83 (b(s(z), s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1122, 7218])).
% 1.65/1.83 tff(7220,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7221,plain,
% 1.65/1.83 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(7222,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[7221])).
% 1.65/1.83 tff(7223,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[7222, 7220])).
% 1.65/1.83 tff(7224,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(7225,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[7224, 7223])).
% 1.65/1.83 tff(7226,plain,
% 1.65/1.83 (~r(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7225, 108, 862, 2240, 2337])).
% 1.65/1.83 tff(7227,plain,
% 1.65/1.83 (b(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[481, 45, 34, 7226])).
% 1.65/1.83 tff(7228,plain,
% 1.65/1.83 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[4313, 108, 130, 862, 2240])).
% 1.65/1.83 tff(7229,plain,
% 1.65/1.83 (b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[440, 7228])).
% 1.65/1.83 tff(7230,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7231,plain,
% 1.65/1.84 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7232,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7231])).
% 1.65/1.84 tff(7233,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[7232, 7230])).
% 1.65/1.84 tff(7234,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7235,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7234, 7233])).
% 1.65/1.84 tff(7236,plain,
% 1.65/1.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7235, 108, 130, 862, 2240])).
% 1.65/1.84 tff(7237,plain,
% 1.65/1.84 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[462, 7236])).
% 1.65/1.84 tff(7238,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7239,plain,
% 1.65/1.84 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7240,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7239])).
% 1.65/1.84 tff(7241,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[7240, 7238])).
% 1.65/1.84 tff(7242,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7243,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7242, 7241])).
% 1.65/1.84 tff(7244,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7243, 233, 1009, 920, 7237, 7229, 7227, 7219])).
% 1.65/1.84 tff(7245,plain,((~r(s(z), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(7246,plain,
% 1.65/1.84 (~r(s(z), s(s(s(z))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7245, 7211, 920, 862, 1009, 130])).
% 1.65/1.84 tff(7247,plain,
% 1.65/1.84 (b(s(z), s(s(s(z))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[323, 45, 320, 7246])).
% 1.65/1.84 tff(7248,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7249,plain,
% 1.65/1.84 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7250,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7249])).
% 1.65/1.84 tff(7251,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[7250, 7248])).
% 1.65/1.84 tff(7252,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7253,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7252, 7251])).
% 1.65/1.84 tff(7254,plain,
% 1.65/1.84 (~b(s(z), z)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7253, 233, 273, 272, 285])).
% 1.65/1.84 tff(7255,plain,
% 1.65/1.84 (r(s(z), z)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[260, 7254])).
% 1.65/1.84 tff(7256,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7257,plain,
% 1.65/1.84 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7258,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7257])).
% 1.65/1.84 tff(7259,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[7258, 7256])).
% 1.65/1.84 tff(7260,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7261,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7260, 7259])).
% 1.65/1.84 tff(7262,plain,
% 1.65/1.84 (~b(s(z), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7261, 233, 919, 272, 285])).
% 1.65/1.84 tff(7263,plain,
% 1.65/1.84 (r(s(z), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[1130, 7262, 954])).
% 1.65/1.84 tff(7264,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7265,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7266,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7265, 7264])).
% 1.65/1.84 tff(7267,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7266, 108, 938, 1059, 7263, 7255])).
% 1.65/1.84 tff(7268,plain,((~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, z)) | (s(z) = elem!1) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(7269,plain,
% 1.65/1.84 (s(z) = elem!1),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7268, 7247, 1059, 938, 273, 7201, 919])).
% 1.65/1.84 tff(7270,plain,
% 1.65/1.84 (s(s(z)) = s(elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7269])).
% 1.65/1.84 tff(7271,plain,
% 1.65/1.84 (s(s(s(z))) = s(s(elem!1))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7270])).
% 1.65/1.84 tff(7272,plain,
% 1.65/1.84 (s(s(elem!1)) = s(s(s(z)))),
% 1.65/1.84 inference(symmetry,[status(thm)],[7271])).
% 1.65/1.84 tff(7273,plain,
% 1.65/1.84 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7272])).
% 1.65/1.84 tff(7274,plain,
% 1.65/1.84 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(symmetry,[status(thm)],[7273])).
% 1.65/1.84 tff(7275,plain,
% 1.65/1.84 (r(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[862, 7274])).
% 1.65/1.84 tff(7276,plain,
% 1.65/1.84 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7271])).
% 1.65/1.84 tff(7277,plain,
% 1.65/1.84 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.65/1.84 inference(symmetry,[status(thm)],[7276])).
% 1.65/1.84 tff(7278,plain,
% 1.65/1.84 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7277, 7272])).
% 1.65/1.84 tff(7279,plain,
% 1.65/1.84 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.84 inference(symmetry,[status(thm)],[7278])).
% 1.65/1.84 tff(7280,plain,
% 1.65/1.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[130, 7279])).
% 1.65/1.84 tff(7281,plain,
% 1.65/1.84 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7276])).
% 1.65/1.84 tff(7282,plain,
% 1.65/1.84 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[4313, 108, 130, 862, 7211])).
% 1.65/1.84 tff(7283,plain,
% 1.65/1.84 (b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[440, 7282])).
% 1.65/1.84 tff(7284,plain,
% 1.65/1.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7235, 108, 130, 862, 7211])).
% 1.65/1.84 tff(7285,plain,
% 1.65/1.84 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[462, 7284])).
% 1.65/1.84 tff(7286,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7287,plain,
% 1.65/1.84 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7288,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7287])).
% 1.65/1.84 tff(7289,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.65/1.84 inference(transitivity,[status(thm)],[7288, 7286])).
% 1.65/1.84 tff(7290,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7291,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7290, 7289])).
% 1.65/1.84 tff(7292,plain,
% 1.65/1.84 (~b(s(s(s(s(z)))), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7291, 233, 1009, 7285, 7283])).
% 1.65/1.84 tff(7293,plain,
% 1.65/1.84 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[949, 7269])).
% 1.65/1.84 tff(7294,plain,
% 1.65/1.84 (~(s(s(s(s(z)))) = elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[855, 7293])).
% 1.65/1.84 tff(7295,plain,
% 1.65/1.84 (r(s(s(s(s(z)))), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[860, 7294, 7292])).
% 1.65/1.84 tff(7296,plain,
% 1.65/1.84 (r(s(s(s(elem!1))), elem!1)),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7295, 7281])).
% 1.65/1.84 tff(7297,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7298,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7299,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7298, 7297])).
% 1.65/1.84 tff(7300,plain,
% 1.65/1.84 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7299, 108, 1059, 7296])).
% 1.65/1.84 tff(7301,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7300, 7280, 7275])).
% 1.65/1.84 tff(7302,plain,((~b(elem!1, s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(7303,plain,
% 1.65/1.84 (~b(elem!1, s(s(s(z))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7302, 7199, 130, 862, 938, 273, 920, 1059])).
% 1.65/1.84 tff(7304,plain,
% 1.65/1.84 (r(elem!1, s(s(s(z))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[886, 7303, 836])).
% 1.65/1.84 tff(7305,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7306,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7307,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7306, 7305])).
% 1.65/1.84 tff(7308,plain,
% 1.65/1.84 (~r(s(z), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7307, 108, 862, 888, 2337])).
% 1.65/1.84 tff(7309,plain,
% 1.65/1.84 (b(s(z), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[1130, 7308, 954])).
% 1.65/1.84 tff(7310,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7311,plain,
% 1.65/1.84 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(7312,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[7311])).
% 1.65/1.84 tff(7313,plain,
% 1.65/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[7312, 7310])).
% 1.65/1.84 tff(7314,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(7315,plain,
% 1.65/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[7314, 7313])).
% 1.65/1.84 tff(7316,plain,
% 1.65/1.84 (~b(s(z), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[7315, 233, 1009, 920, 7309])).
% 1.65/1.84 tff(7317,plain,
% 1.65/1.84 (r(s(z), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[481, 45, 34, 7316])).
% 1.65/1.84 tff(7318,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7319,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7320,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7319, 7318])).
% 1.65/1.85 tff(7321,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7320, 108, 701, 492, 2337, 7317])).
% 1.65/1.85 tff(7322,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(7323,plain,
% 1.65/1.85 (~r(s(z), s(s(s(z))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7322, 954, 492, 1009, 920, 701, 862, 888])).
% 1.65/1.85 tff(7324,plain,
% 1.65/1.85 (b(s(z), s(s(s(z))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[323, 45, 320, 7323])).
% 1.65/1.85 tff(7325,plain,
% 1.65/1.85 (~b(s(z), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7253, 233, 273, 7201, 7324])).
% 1.65/1.85 tff(7326,plain,
% 1.65/1.85 (r(s(z), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[260, 7325])).
% 1.65/1.85 tff(7327,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7328,plain,
% 1.65/1.85 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7329,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), z))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7328])).
% 1.65/1.85 tff(7330,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[7329, 7327])).
% 1.65/1.85 tff(7331,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7332,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), z))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7331, 7330])).
% 1.65/1.85 tff(7333,plain,
% 1.65/1.85 (~r(s(z), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7332, 108, 938, 701, 7326])).
% 1.65/1.85 tff(7334,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7335,plain,
% 1.65/1.85 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7336,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7335])).
% 1.65/1.85 tff(7337,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[7336, 7334])).
% 1.65/1.85 tff(7338,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7339,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7338, 7337])).
% 1.65/1.85 tff(7340,plain,
% 1.65/1.85 (~r(s(z), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7339, 108, 938, 1059, 7326])).
% 1.65/1.85 tff(7341,plain,
% 1.65/1.85 (b(s(z), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1130, 7340, 954])).
% 1.65/1.85 tff(7342,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7343,plain,
% 1.65/1.85 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7344,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7343])).
% 1.65/1.85 tff(7345,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.85 inference(transitivity,[status(thm)],[7344, 7342])).
% 1.65/1.85 tff(7346,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7347,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7346, 7345])).
% 1.65/1.85 tff(7348,plain,
% 1.65/1.85 (~b(s(z), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7347, 233, 80, 272, 285])).
% 1.65/1.85 tff(7349,plain,
% 1.65/1.85 (r(s(z), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[481, 45, 34, 7348])).
% 1.65/1.85 tff(7350,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7332, 108, 938, 701, 7255, 7349])).
% 1.65/1.85 tff(7351,plain,((~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(7352,plain,
% 1.65/1.85 (~b(s(s(z)), s(s(s(z))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7351, 7324, 701, 273, 7201, 938])).
% 1.65/1.85 tff(7353,plain,
% 1.65/1.85 (r(s(s(z)), s(s(s(z))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2228, 7352])).
% 1.65/1.85 tff(7354,plain,
% 1.65/1.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[4313, 108, 130, 862, 7353])).
% 1.65/1.85 tff(7355,plain,
% 1.65/1.85 (b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[440, 7354])).
% 1.65/1.85 tff(7356,plain,
% 1.65/1.85 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7235, 108, 130, 862, 7353])).
% 1.65/1.85 tff(7357,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[462, 7356])).
% 1.65/1.85 tff(7358,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7359,plain,
% 1.65/1.85 (((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7360,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7359])).
% 1.65/1.85 tff(7361,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.65/1.85 inference(transitivity,[status(thm)],[7360, 7358])).
% 1.65/1.85 tff(7362,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7363,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7362, 7361])).
% 1.65/1.85 tff(7364,plain,
% 1.65/1.85 (~b(s(z), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7363, 233, 1009, 920, 7357, 7355, 7341])).
% 1.65/1.85 tff(7365,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[481, 45, 34, 7364, 7333])).
% 1.65/1.85 tff(7366,plain,((s(z) = elem!1) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(7367,plain,
% 1.65/1.85 (s(z) = elem!1),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7366, 7199, 920, 938, 701, 1059, 130, 862, 273, 492, 7304])).
% 1.65/1.85 tff(7368,plain,
% 1.65/1.85 (s(s(z)) = s(elem!1)),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7367])).
% 1.65/1.85 tff(7369,plain,
% 1.65/1.85 (s(s(s(z))) = s(s(elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7368])).
% 1.65/1.85 tff(7370,plain,
% 1.65/1.85 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7369])).
% 1.65/1.85 tff(7371,plain,
% 1.65/1.85 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.65/1.85 inference(symmetry,[status(thm)],[7370])).
% 1.65/1.85 tff(7372,plain,
% 1.65/1.85 (s(elem!1) = s(s(z))),
% 1.65/1.85 inference(symmetry,[status(thm)],[7368])).
% 1.65/1.85 tff(7373,plain,
% 1.65/1.85 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7372, 7371])).
% 1.65/1.85 tff(7374,plain,
% 1.65/1.85 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7373])).
% 1.65/1.85 tff(7375,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7370])).
% 1.65/1.85 tff(7376,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7377,plain,
% 1.65/1.85 (((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7378,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7377])).
% 1.65/1.85 tff(7379,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.65/1.85 inference(transitivity,[status(thm)],[7378, 7376])).
% 1.65/1.85 tff(7380,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7381,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7380, 7379])).
% 1.65/1.85 tff(7382,plain,
% 1.65/1.85 (~r(s(s(s(s(z)))), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7381, 108, 130, 862, 7304])).
% 1.65/1.85 tff(7383,plain,
% 1.65/1.85 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[949, 7367])).
% 1.65/1.85 tff(7384,plain,
% 1.65/1.85 (~(s(s(s(s(z)))) = elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[855, 7383])).
% 1.65/1.85 tff(7385,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[860, 7384, 7382])).
% 1.65/1.85 tff(7386,plain,
% 1.65/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7385, 7375])).
% 1.65/1.85 tff(7387,plain,
% 1.65/1.85 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7368])).
% 1.65/1.85 tff(7388,plain,
% 1.65/1.85 (b(s(elem!1), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[920, 7387])).
% 1.65/1.85 tff(7389,plain,
% 1.65/1.85 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7370])).
% 1.65/1.85 tff(7390,plain,
% 1.65/1.85 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7172, 108, 130, 862, 7304])).
% 1.65/1.85 tff(7391,plain,
% 1.65/1.85 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[850, 7383, 7390])).
% 1.65/1.85 tff(7392,plain,
% 1.65/1.85 (b(elem!1, s(s(s(elem!1))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7391, 7389])).
% 1.65/1.85 tff(7393,plain,
% 1.65/1.85 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7394,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7393])).
% 1.65/1.85 tff(7395,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[7394, 6507])).
% 1.65/1.85 tff(7396,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7397,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7396, 7395])).
% 1.65/1.85 tff(7398,plain,
% 1.65/1.85 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7397, 233, 7392, 7388, 7386])).
% 1.65/1.85 tff(7399,plain,
% 1.65/1.85 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7398, 7374])).
% 1.65/1.85 tff(7400,plain,
% 1.65/1.85 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7371, 7372])).
% 1.65/1.85 tff(7401,plain,
% 1.65/1.85 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7400])).
% 1.65/1.85 tff(7402,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7403,plain,
% 1.65/1.85 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(7404,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[7403])).
% 1.65/1.85 tff(7405,plain,
% 1.65/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[7404, 7402])).
% 1.65/1.85 tff(7406,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(7407,plain,
% 1.65/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[7406, 7405])).
% 1.65/1.85 tff(7408,plain,
% 1.65/1.85 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7407, 233, 7392, 7388, 7386])).
% 1.65/1.86 tff(7409,plain,
% 1.65/1.86 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7408, 7401])).
% 1.65/1.86 tff(7410,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1928, 7409, 7399, 130, 492])).
% 1.65/1.86 tff(7411,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(7412,plain,
% 1.65/1.86 (~r(s(s(z)), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7411, 7194, 3699, 4307, 7195, 4555, 862, 273, 7192, 4727])).
% 1.65/1.86 tff(7413,plain,
% 1.65/1.86 (b(s(s(z)), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[374, 7412])).
% 1.65/1.86 tff(7414,plain,
% 1.65/1.86 (~b(s(s(z)), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[657, 7413, 273, 7197])).
% 1.65/1.86 tff(7415,plain,
% 1.65/1.86 (r(s(s(z)), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[2228, 7414])).
% 1.65/1.86 tff(7416,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7417,plain,
% 1.65/1.86 (((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7418,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7417])).
% 1.65/1.86 tff(7419,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[7418, 7416])).
% 1.65/1.86 tff(7420,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7421,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7420, 7419])).
% 1.65/1.86 tff(7422,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7421, 108, 994, 862, 492, 2240])).
% 1.65/1.86 tff(7423,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(7424,plain,
% 1.65/1.86 (~r(elem!1, s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7423, 7415, 3699, 862])).
% 1.65/1.86 tff(7425,plain,
% 1.65/1.86 (b(elem!1, s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1236, 7424, 4727])).
% 1.65/1.86 tff(7426,plain,
% 1.65/1.86 (~b(elem!1, s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7302, 7425, 4307, 862, 7195, 273, 7194, 4555])).
% 1.65/1.86 tff(7427,plain,
% 1.65/1.86 (r(elem!1, s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[886, 7426, 7192])).
% 1.65/1.86 tff(7428,plain,
% 1.65/1.86 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7172, 108, 4307, 862, 7427])).
% 1.65/1.86 tff(7429,plain,
% 1.65/1.86 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7235, 108, 4307, 862, 7415])).
% 1.65/1.86 tff(7430,plain,
% 1.65/1.86 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[462, 7429])).
% 1.65/1.86 tff(7431,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7432,plain,
% 1.65/1.86 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7433,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7432])).
% 1.65/1.86 tff(7434,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[7433, 7431])).
% 1.65/1.86 tff(7435,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7436,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7435, 7434])).
% 1.65/1.86 tff(7437,plain,
% 1.65/1.86 (~b(elem!1, s(s(s(s(z)))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7436, 233, 7425, 7194, 7430])).
% 1.65/1.86 tff(7438,plain,
% 1.65/1.86 (elem!1 = s(s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[850, 7437, 7428])).
% 1.65/1.86 tff(7439,plain,
% 1.65/1.86 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7438])).
% 1.65/1.86 tff(7440,plain,
% 1.65/1.86 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.86 inference(symmetry,[status(thm)],[7439])).
% 1.65/1.86 tff(7441,plain,
% 1.65/1.86 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7440])).
% 1.65/1.86 tff(7442,plain,
% 1.65/1.86 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[576, 7441])).
% 1.65/1.86 tff(7443,plain,
% 1.65/1.86 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7438])).
% 1.65/1.86 tff(7444,plain,
% 1.65/1.86 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7443])).
% 1.65/1.86 tff(7445,plain,
% 1.65/1.86 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7444])).
% 1.65/1.86 tff(7446,plain,
% 1.65/1.86 (~(s(elem!1) = s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[5196, 4727])).
% 1.65/1.86 tff(7447,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7448,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7449,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7448, 7447])).
% 1.65/1.86 tff(7450,plain,
% 1.65/1.86 (~r(s(elem!1), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7449, 108, 1059, 862, 5153])).
% 1.65/1.86 tff(7451,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7452,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7453,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7452, 7451])).
% 1.65/1.86 tff(7454,plain,
% 1.65/1.86 (b(s(elem!1), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7453, 45, 5201, 7450])).
% 1.65/1.86 tff(7455,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7456,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7457,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7456, 7455])).
% 1.65/1.86 tff(7458,plain,
% 1.65/1.86 (~r(s(elem!1), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7457, 108, 938, 1059, 5153])).
% 1.65/1.86 tff(7459,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7460,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7461,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7460, 7459])).
% 1.65/1.86 tff(7462,plain,
% 1.65/1.86 (b(s(elem!1), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7461, 45, 1346, 7458])).
% 1.65/1.86 tff(7463,plain,
% 1.65/1.86 (b(s(s(s(z))), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[243, 45, 65, 7200])).
% 1.65/1.86 tff(7464,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7465,plain,
% 1.65/1.86 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7466,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7465])).
% 1.65/1.86 tff(7467,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[7466, 7464])).
% 1.65/1.86 tff(7468,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7469,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7468, 7467])).
% 1.65/1.86 tff(7470,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7469, 233, 273, 7463, 7462, 7454])).
% 1.65/1.86 tff(7471,plain,((~r(s(elem!1), elem!1)) | (~b(z, s(s(s(z))))) | (s(elem!1) = s(s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(7472,plain,
% 1.65/1.86 (~r(s(elem!1), elem!1)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7471, 4555, 862, 7446, 7195, 273])).
% 1.65/1.86 tff(7473,plain,
% 1.65/1.86 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7472, 7445])).
% 1.65/1.86 tff(7474,plain,
% 1.65/1.86 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7438])).
% 1.65/1.86 tff(7475,plain,
% 1.65/1.86 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.86 inference(symmetry,[status(thm)],[7474])).
% 1.65/1.86 tff(7476,plain,
% 1.65/1.86 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7443, 7438])).
% 1.65/1.86 tff(7477,plain,
% 1.65/1.86 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.86 inference(transitivity,[status(thm)],[7476, 7475])).
% 1.65/1.86 tff(7478,plain,
% 1.65/1.86 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7477])).
% 1.65/1.86 tff(7479,plain,
% 1.65/1.86 (~r(s(z), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7245, 7425, 7194, 862, 7415, 4307])).
% 1.65/1.86 tff(7480,plain,
% 1.65/1.86 (~(s(z) = elem!1)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7155, 7479, 7427])).
% 1.65/1.86 tff(7481,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7482,plain,
% 1.65/1.86 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7483,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7482])).
% 1.65/1.86 tff(7484,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.65/1.86 inference(transitivity,[status(thm)],[7483, 7481])).
% 1.65/1.86 tff(7485,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7486,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7485, 7484])).
% 1.65/1.86 tff(7487,plain,
% 1.65/1.86 (~b(s(s(z)), s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7486, 233, 1009, 920, 1289])).
% 1.65/1.86 tff(7488,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 1.65/1.86 tff(7489,plain,
% 1.65/1.86 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7488])).
% 1.65/1.86 tff(7490,plain,
% 1.65/1.86 (s(z) = elem!1),
% 1.65/1.86 inference(transitivity,[status(thm)],[21, 7489, 719])).
% 1.65/1.86 tff(7491,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[954, 7490])).
% 1.65/1.86 tff(7492,plain,((~(s(s(z)) = s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(7493,plain,
% 1.65/1.86 (~(s(s(z)) = s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7492, 954])).
% 1.65/1.86 tff(7494,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7495,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7496,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7495, 7494])).
% 1.65/1.86 tff(7497,plain,
% 1.65/1.86 (r(s(s(z)), s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7496, 45, 7493, 7487])).
% 1.65/1.86 tff(7498,plain,
% 1.65/1.86 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.65/1.86 inference(commutativity,[status(thm)],[])).
% 1.65/1.86 tff(7499,plain,
% 1.65/1.86 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 1.65/1.86 inference(symmetry,[status(thm)],[7498])).
% 1.65/1.86 tff(7500,plain,
% 1.65/1.86 ((~(s(s(z)) = s(elem!1))) <=> (~(s(elem!1) = s(s(z))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7499])).
% 1.65/1.86 tff(7501,plain,
% 1.65/1.86 (~(s(elem!1) = s(s(z)))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7493, 7500])).
% 1.65/1.86 tff(7502,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7503,plain,
% 1.65/1.86 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7504,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7503])).
% 1.65/1.86 tff(7505,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[7504, 7502])).
% 1.65/1.86 tff(7506,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7507,plain,
% 1.65/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7506, 7505])).
% 1.65/1.86 tff(7508,plain,
% 1.65/1.86 (~b(s(elem!1), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7507, 233, 1009, 920, 1289])).
% 1.65/1.86 tff(7509,plain,
% 1.65/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7510,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7511,plain,
% 1.65/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7510, 7509])).
% 1.65/1.86 tff(7512,plain,
% 1.65/1.86 ((s(elem!1) = s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7511, 45, 7508])).
% 1.65/1.86 tff(7513,plain,
% 1.65/1.86 (r(s(elem!1), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7512, 7501])).
% 1.65/1.86 tff(7514,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7515,plain,
% 1.65/1.86 (((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7516,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(z))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[7515])).
% 1.65/1.86 tff(7517,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[7516, 7514])).
% 1.65/1.86 tff(7518,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(7519,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(s(z))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[7518, 7517])).
% 1.65/1.86 tff(7520,plain,
% 1.65/1.86 (~r(s(elem!1), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7519, 108, 3699, 7513, 7497])).
% 1.65/1.86 tff(7521,plain,
% 1.65/1.86 (b(s(elem!1), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[7453, 45, 5201, 7520])).
% 1.65/1.86 tff(7522,plain,
% 1.65/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(7523,plain,
% 1.65/1.86 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7524,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7523])).
% 1.65/1.87 tff(7525,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[7524, 7522])).
% 1.65/1.87 tff(7526,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(elem!1))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7527,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7526, 7525])).
% 1.65/1.87 tff(7528,plain,
% 1.65/1.87 (~b(z, s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7527, 233, 273, 7201, 7521])).
% 1.65/1.87 tff(7529,plain,
% 1.65/1.87 ((z = s(elem!1)) | r(z, s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[4473, 45, 7528])).
% 1.65/1.87 tff(7530,plain,
% 1.65/1.87 (r(z, s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7529, 4458])).
% 1.65/1.87 tff(7531,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7532,plain,
% 1.65/1.87 (((~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7533,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7532])).
% 1.65/1.87 tff(7534,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[7533, 7531])).
% 1.65/1.87 tff(7535,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), z)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7536,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7535, 7534])).
% 1.65/1.87 tff(7537,plain,
% 1.65/1.87 (~r(s(s(z)), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7536, 108, 7513, 7497, 7530])).
% 1.65/1.87 tff(7538,plain,
% 1.65/1.87 (b(s(s(z)), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[372, 45, 32, 7537])).
% 1.65/1.87 tff(7539,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7540,plain,
% 1.65/1.87 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7541,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7540])).
% 1.65/1.87 tff(7542,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[7541, 7539])).
% 1.65/1.87 tff(7543,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(z)))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7544,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7543, 7542])).
% 1.65/1.87 tff(7545,plain,
% 1.65/1.87 (~r(z, s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7544, 108, 7513, 7497, 7530])).
% 1.65/1.87 tff(7546,plain,
% 1.65/1.87 (b(z, s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[357, 45, 7545, 352])).
% 1.65/1.87 tff(7547,assumption,(b(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.65/1.87 tff(7548,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7549,plain,
% 1.65/1.87 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7550,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7549])).
% 1.65/1.87 tff(7551,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[7550, 7548])).
% 1.65/1.87 tff(7552,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7553,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7552, 7551])).
% 1.65/1.87 tff(7554,plain,
% 1.65/1.87 (~b(s(z), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7553, 233, 272, 7547, 285])).
% 1.65/1.87 tff(7555,plain,
% 1.65/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7556,plain,
% 1.65/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7557,plain,
% 1.65/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7556, 7555])).
% 1.65/1.87 tff(7558,plain,
% 1.65/1.87 (r(s(z), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7557, 45, 1309, 7554])).
% 1.65/1.87 tff(7559,plain,
% 1.65/1.87 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7560,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7559])).
% 1.65/1.87 tff(7561,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[7560, 7464])).
% 1.65/1.87 tff(7562,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7563,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(z)))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7562, 7561])).
% 1.65/1.87 tff(7564,plain,
% 1.65/1.87 (~b(s(elem!1), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7563, 233, 273, 272, 7547])).
% 1.65/1.87 tff(7565,plain,
% 1.65/1.87 (r(s(elem!1), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7461, 45, 1346, 7564])).
% 1.65/1.87 tff(7566,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7567,plain,
% 1.65/1.87 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7568,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7567])).
% 1.65/1.87 tff(7569,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[7568, 7566])).
% 1.65/1.87 tff(7570,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7571,plain,
% 1.65/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7570, 7569])).
% 1.65/1.87 tff(7572,plain,
% 1.65/1.87 (~b(s(z), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7571, 233, 273, 706, 649, 272, 285])).
% 1.65/1.87 tff(7573,plain,
% 1.65/1.87 (r(s(z), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[260, 7572])).
% 1.65/1.87 tff(7574,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(7575,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(7576,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7575, 7574])).
% 1.65/1.87 tff(7577,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7576, 108, 938, 7573, 7565, 7558])).
% 1.65/1.87 tff(7578,plain,((~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (s(z) = s(elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(7579,plain,
% 1.65/1.87 (~b(s(z), s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7578, 7521, 1309, 7201, 938, 273, 7546, 7538])).
% 1.65/1.87 tff(7580,plain,
% 1.65/1.87 (r(s(z), s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[323, 45, 320, 7579])).
% 1.65/1.87 tff(7581,plain,
% 1.65/1.87 (r(s(s(s(z))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[339, 177, 3698])).
% 1.65/1.87 tff(7582,plain,
% 1.65/1.87 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[824])).
% 1.65/1.87 tff(7583,plain,
% 1.65/1.87 (r(z, s(s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[938, 7582])).
% 1.65/1.87 tff(7584,plain,
% 1.65/1.87 (~r(s(s(s(s(z)))), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[3333, 108, 130, 492, 7583])).
% 1.65/1.87 tff(7585,plain,
% 1.65/1.87 (b(s(s(s(s(z)))), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[629, 45, 89, 7584])).
% 1.65/1.87 tff(7586,plain,
% 1.65/1.87 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[2266, 233, 706, 649, 7585])).
% 1.65/1.87 tff(7587,plain,
% 1.65/1.87 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[2256, 233, 706, 649, 7585])).
% 1.65/1.87 tff(7588,plain,
% 1.65/1.87 (s(s(z)) = s(s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1927, 7587, 492, 130, 7586])).
% 1.65/1.87 tff(7589,plain,
% 1.65/1.87 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7588])).
% 1.65/1.87 tff(7590,plain,
% 1.65/1.87 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(symmetry,[status(thm)],[7589])).
% 1.65/1.87 tff(7591,plain,
% 1.65/1.87 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[7590])).
% 1.65/1.87 tff(7592,plain,
% 1.65/1.87 (~b(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[4306, 7591])).
% 1.65/1.87 tff(7593,plain,
% 1.65/1.87 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[824])).
% 1.65/1.87 tff(7594,plain,
% 1.65/1.87 (b(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[920, 7593])).
% 1.65/1.87 tff(7595,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7594, 7592])).
% 1.65/1.87 tff(7596,plain,((~(elem!1 = s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(7597,plain,
% 1.65/1.87 (~(elem!1 = s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7596, 7581, 4306, 130, 706, 649, 920, 938])).
% 1.65/1.87 tff(7598,plain,
% 1.65/1.87 (r(elem!1, s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[886, 7597, 873])).
% 1.65/1.87 tff(7599,plain,
% 1.65/1.87 (~r(s(s(s(z))), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1067, 7598, 1059, 938])).
% 1.65/1.87 tff(7600,plain,
% 1.65/1.87 (b(s(s(s(z))), z)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[243, 45, 65, 7599])).
% 1.65/1.87 tff(7601,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.65/1.87 tff(7602,plain,
% 1.65/1.87 (~(s(s(z)) = s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[2222, 177])).
% 1.65/1.87 tff(7603,plain,
% 1.65/1.87 (b(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[2227, 7602, 7601])).
% 1.65/1.87 tff(7604,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[3952, 233, 7603, 706, 649, 7600])).
% 1.65/1.87 tff(7605,plain,((s(s(s(z))) = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | r(s(s(z)), s(s(s(z)))) | b(elem!1, s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | b(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(7606,plain,
% 1.65/1.87 ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(elem!1, z)) | (~r(z, elem!1)) | r(s(s(z)), s(s(s(z)))) | b(elem!1, s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | b(s(s(s(z))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7605, 171])).
% 1.65/1.87 tff(7607,plain,
% 1.65/1.87 (r(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7606, 7538, 3698, 938, 1059, 873, 4306, 4307, 920, 7546])).
% 1.65/1.87 tff(7608,plain,
% 1.65/1.87 (~r(s(z), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7225, 108, 862, 7607, 7580])).
% 1.65/1.87 tff(7609,plain,
% 1.65/1.87 (b(s(z), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[481, 45, 34, 7608])).
% 1.65/1.87 tff(7610,plain,
% 1.65/1.87 (~r(s(z), elem!1)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7307, 108, 862, 888, 7580])).
% 1.65/1.87 tff(7611,plain,
% 1.65/1.87 (b(s(z), elem!1)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1130, 7610, 954])).
% 1.65/1.87 tff(7612,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7315, 233, 1009, 920, 7611, 7609])).
% 1.65/1.87 tff(7613,plain,((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (s(z) = s(elem!1)) | (~r(z, elem!1)) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(s(z))) | (~r(elem!1, z)) | b(elem!1, s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | (s(elem!1) = s(s(s(z)))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(7614,plain,
% 1.65/1.87 (~b(s(elem!1), elem!1)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7613, 7480, 7194, 862, 7425, 726, 7195, 273, 3698, 4555, 7426, 4306, 7446, 7427])).
% 1.65/1.87 tff(7615,plain,
% 1.65/1.87 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[7614, 7478])).
% 1.65/1.87 tff(7616,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[5077, 7615, 7473, 7442])).
% 1.65/1.87 tff(7617,plain,((z = elem!1) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(s(z))) | b(s(s(s(s(z)))), s(s(s(z)))) | (s(s(z)) = elem!1) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(7618,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7617, 7190, 7184, 273, 3698, 7166, 4306, 717, 7180])).
% 1.65/1.87 tff(7619,plain,((s(s(s(z))) = elem!1) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(s(z))) | b(s(s(s(s(z)))), s(s(s(z)))) | (z = elem!1) | b(s(s(s(s(z)))), z) | b(z, s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | r(elem!1, s(z)) | r(s(z), s(s(s(z)))) | b(elem!1, s(s(s(z)))) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(7620,plain,
% 1.65/1.87 (b(elem!1, s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7619, 7149, 3698, 4306, 717, 7148, 217, 442, 424, 2854, 203, 1357, 7147, 1049, 273])).
% 1.65/1.87 tff(7621,plain,
% 1.65/1.87 (~(s(s(z)) = elem!1)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[4767, 7620, 4303])).
% 1.65/1.87 tff(7622,plain,
% 1.65/1.87 (~(elem!1 = s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1697, 7621])).
% 1.65/1.87 tff(7623,plain,
% 1.65/1.87 (r(s(s(s(z))), elem!1)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[843, 7149, 1049])).
% 1.65/1.87 tff(7624,plain,
% 1.65/1.87 (~r(elem!1, s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7423, 7623, 3699, 4305])).
% 1.65/1.87 tff(7625,plain,
% 1.65/1.87 (b(elem!1, s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1236, 7624, 7622])).
% 1.65/1.87 tff(7626,plain,
% 1.65/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7627,plain,
% 1.65/1.88 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7628,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7627])).
% 1.65/1.88 tff(7629,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z)))),
% 1.65/1.88 inference(transitivity,[status(thm)],[7628, 7626])).
% 1.65/1.88 tff(7630,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(7631,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7630, 7629])).
% 1.65/1.88 tff(7632,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7631, 233, 809, 7625, 273, 649])).
% 1.65/1.88 tff(7633,plain,((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | b(s(s(z)), s(s(s(z)))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), s(s(z))) | b(s(s(s(s(z)))), s(s(s(z)))) | (z = elem!1) | b(z, s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | r(elem!1, s(z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(7634,plain,
% 1.65/1.88 (~b(elem!1, z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7633, 7136, 6973, 4303, 6975, 3698, 4306, 6998, 6996, 6977, 6971, 2854, 7145, 1357, 7003])).
% 1.65/1.88 tff(7635,plain,
% 1.65/1.88 (r(elem!1, z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[1037, 1033, 1632])).
% 1.65/1.88 tff(7636,plain,
% 1.65/1.88 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.65/1.88 inference(monotonicity,[status(thm)],[1677])).
% 1.65/1.88 tff(7637,plain,
% 1.65/1.88 (r(elem!1, z) <=> r(s(s(z)), z)),
% 1.65/1.88 inference(symmetry,[status(thm)],[7636])).
% 1.65/1.88 tff(7638,plain,
% 1.65/1.88 (r(s(s(z)), z)),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[1059, 7637])).
% 1.65/1.88 tff(7639,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[369, 7638])).
% 1.65/1.88 tff(7640,plain,((~(s(s(z)) = elem!1)) | r(s(s(z)), z) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(7641,plain,
% 1.65/1.88 (~(s(s(z)) = elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7640, 7635, 369])).
% 1.65/1.88 tff(7642,plain,
% 1.65/1.88 (~r(s(s(s(z))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7617, 7641, 273, 3698, 1033, 4306, 717, 1027])).
% 1.65/1.88 tff(7643,plain,
% 1.65/1.88 (b(s(s(s(z))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[843, 7642, 1049])).
% 1.65/1.88 tff(7644,plain,
% 1.65/1.88 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[6584, 7643, 5996])).
% 1.65/1.88 tff(7645,plain,
% 1.65/1.88 (r(z, elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[934, 1027, 717])).
% 1.65/1.88 tff(7646,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7647,plain,
% 1.65/1.88 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7648,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7647])).
% 1.65/1.88 tff(7649,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.88 inference(transitivity,[status(thm)],[7648, 7646])).
% 1.65/1.88 tff(7650,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(7651,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7650, 7649])).
% 1.65/1.88 tff(7652,plain,
% 1.65/1.88 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7651, 108, 7645, 7635, 3244])).
% 1.65/1.88 tff(7653,plain,
% 1.65/1.88 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[850, 7652, 7644])).
% 1.65/1.88 tff(7654,plain,
% 1.65/1.88 (~(s(s(s(s(z)))) = elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[855, 7644])).
% 1.65/1.88 tff(7655,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7656,plain,
% 1.65/1.88 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7657,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7656])).
% 1.65/1.88 tff(7658,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.88 inference(transitivity,[status(thm)],[7657, 7655])).
% 1.65/1.88 tff(7659,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(7660,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7659, 7658])).
% 1.65/1.88 tff(7661,plain,
% 1.65/1.88 (~r(s(s(s(s(z)))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7660, 108, 7645, 7635, 3244])).
% 1.65/1.88 tff(7662,plain,
% 1.65/1.88 (b(s(s(s(s(z)))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[860, 7661, 7654])).
% 1.65/1.88 tff(7663,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7664,plain,
% 1.65/1.88 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7665,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7664])).
% 1.65/1.88 tff(7666,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[7665, 7663])).
% 1.65/1.88 tff(7667,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(7668,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7667, 7666])).
% 1.65/1.88 tff(7669,plain,
% 1.65/1.88 (~b(elem!1, s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7668, 233, 7643, 7662, 7653, 2854, 285])).
% 1.65/1.88 tff(7670,plain,
% 1.65/1.88 (elem!1 = s(z)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[965, 7669, 1357])).
% 1.65/1.88 tff(7671,plain,
% 1.65/1.88 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7670])).
% 1.65/1.88 tff(7672,plain,
% 1.65/1.88 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(symmetry,[status(thm)],[7671])).
% 1.65/1.88 tff(7673,plain,
% 1.65/1.88 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7672])).
% 1.65/1.88 tff(7674,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.65/1.88 tff(7675,plain,
% 1.65/1.88 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7674, 7673])).
% 1.65/1.88 tff(7676,plain,
% 1.65/1.88 (~r(s(z), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7339, 108, 7645, 7635, 246])).
% 1.65/1.88 tff(7677,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7678,plain,
% 1.65/1.88 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7679,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7678])).
% 1.65/1.88 tff(7680,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[7679, 7677])).
% 1.65/1.88 tff(7681,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(7682,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7681, 7680])).
% 1.65/1.88 tff(7683,plain,
% 1.65/1.88 (~b(s(z), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7682, 233, 7662, 7653, 2854])).
% 1.65/1.88 tff(7684,plain,
% 1.65/1.88 (s(z) = elem!1),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[1130, 7683, 7676])).
% 1.65/1.88 tff(7685,plain,
% 1.65/1.88 (s(z) = s(s(s(s(s(z)))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[943, 1264])).
% 1.65/1.88 tff(7686,plain,
% 1.65/1.88 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7685])).
% 1.65/1.88 tff(7687,plain,
% 1.65/1.88 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7686])).
% 1.65/1.88 tff(7688,plain,
% 1.65/1.88 (s(s(z)) = s(elem!1)),
% 1.65/1.88 inference(monotonicity,[status(thm)],[943])).
% 1.65/1.88 tff(7689,plain,
% 1.65/1.88 (s(s(s(z))) = s(s(elem!1))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7688])).
% 1.65/1.88 tff(7690,plain,
% 1.65/1.88 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7689])).
% 1.65/1.88 tff(7691,plain,
% 1.65/1.88 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7690])).
% 1.65/1.88 tff(7692,plain,
% 1.65/1.88 (s(s(s(elem!1))) = z),
% 1.65/1.88 inference(transitivity,[status(thm)],[7691, 86, 7687, 15])).
% 1.65/1.88 tff(7693,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[5287, 7692])).
% 1.65/1.88 tff(7694,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(7695,plain,
% 1.65/1.88 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7694, 7684])).
% 1.65/1.88 tff(7696,plain,
% 1.65/1.88 (s(s(elem!1)) = s(s(s(z)))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7689])).
% 1.65/1.88 tff(7697,plain,
% 1.65/1.88 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7696, 7691])).
% 1.65/1.88 tff(7698,plain,
% 1.65/1.88 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7697])).
% 1.65/1.88 tff(7699,plain,
% 1.65/1.88 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[81, 7698])).
% 1.65/1.88 tff(7700,plain,
% 1.65/1.88 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7691])).
% 1.65/1.88 tff(7701,plain,
% 1.65/1.88 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[7700, 737])).
% 1.65/1.88 tff(7702,plain,
% 1.65/1.88 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7701])).
% 1.65/1.88 tff(7703,plain,
% 1.65/1.88 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(z)))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7702])).
% 1.65/1.88 tff(7704,plain,
% 1.65/1.88 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[576, 7703])).
% 1.65/1.88 tff(7705,plain,
% 1.65/1.88 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7691])).
% 1.65/1.88 tff(7706,plain,
% 1.65/1.88 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7705])).
% 1.65/1.88 tff(7707,plain,
% 1.65/1.88 (b(elem!1, s(s(s(elem!1))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[6197, 7706])).
% 1.65/1.88 tff(7708,plain,
% 1.65/1.88 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7691])).
% 1.65/1.88 tff(7709,plain,
% 1.65/1.88 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.65/1.88 inference(symmetry,[status(thm)],[7708])).
% 1.65/1.88 tff(7710,plain,
% 1.65/1.88 (b(s(s(s(elem!1))), elem!1)),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[1071, 7709])).
% 1.65/1.88 tff(7711,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7712,plain,
% 1.65/1.88 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7713,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7712])).
% 1.65/1.88 tff(7714,plain,
% 1.65/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[7713, 7711])).
% 1.65/1.88 tff(7715,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(7716,plain,
% 1.65/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7715, 7714])).
% 1.65/1.88 tff(7717,plain,
% 1.65/1.88 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7716, 233, 5081])).
% 1.65/1.88 tff(7718,plain,
% 1.65/1.88 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7717, 7710, 7707])).
% 1.65/1.88 tff(7719,plain,
% 1.65/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(7720,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(7721,plain,
% 1.65/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[7720, 7719])).
% 1.65/1.88 tff(7722,plain,
% 1.65/1.88 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7721, 45, 7718])).
% 1.65/1.88 tff(7723,plain,
% 1.65/1.88 (r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7722, 7704])).
% 1.65/1.88 tff(7724,plain,
% 1.65/1.88 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.65/1.88 inference(commutativity,[status(thm)],[])).
% 1.65/1.88 tff(7725,plain,
% 1.65/1.88 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7724])).
% 1.65/1.88 tff(7726,plain,
% 1.65/1.88 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[7725])).
% 1.65/1.88 tff(7727,plain,
% 1.65/1.88 (s(elem!1) = s(s(z))),
% 1.65/1.88 inference(symmetry,[status(thm)],[7688])).
% 1.65/1.88 tff(7728,plain,
% 1.65/1.89 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7727])).
% 1.65/1.89 tff(7729,plain,
% 1.65/1.89 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.65/1.89 inference(symmetry,[status(thm)],[7728])).
% 1.65/1.89 tff(7730,plain,
% 1.65/1.89 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7729])).
% 1.65/1.89 tff(7731,plain,
% 1.65/1.89 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[169, 7730])).
% 1.65/1.89 tff(7732,assumption,(s(s(s(s(s(z))))) = s(s(elem!1))), introduced(assumption)).
% 1.65/1.89 tff(7733,plain,
% 1.65/1.89 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7732])).
% 1.65/1.89 tff(7734,plain,
% 1.65/1.89 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 1.65/1.89 inference(symmetry,[status(thm)],[7733])).
% 1.65/1.89 tff(7735,plain,
% 1.65/1.89 (s(elem!1) = s(s(s(s(z))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[1343, 7734, 85])).
% 1.65/1.89 tff(7736,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 1.65/1.89 tff(7737,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7736, 7735])).
% 1.65/1.89 tff(7738,plain,((~(s(s(s(s(s(z))))) = s(s(elem!1)))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(7739,plain,
% 1.65/1.89 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7738, 7731])).
% 1.65/1.89 tff(7740,plain,
% 1.65/1.89 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7739, 7726])).
% 1.65/1.89 tff(7741,plain,
% 1.65/1.89 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7696])).
% 1.65/1.89 tff(7742,plain,
% 1.65/1.89 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.65/1.89 inference(symmetry,[status(thm)],[7741])).
% 1.65/1.89 tff(7743,plain,
% 1.65/1.89 (b(s(s(elem!1)), elem!1)),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[707, 7742])).
% 1.65/1.89 tff(7744,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7745,plain,
% 1.65/1.89 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7746,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7745])).
% 1.65/1.89 tff(7747,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[7746, 7744])).
% 1.65/1.89 tff(7748,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7749,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7748, 7747])).
% 1.65/1.89 tff(7750,plain,
% 1.65/1.89 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7749, 233, 5081])).
% 1.65/1.89 tff(7751,plain,
% 1.65/1.89 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7750, 7743, 7707])).
% 1.65/1.89 tff(7752,plain,
% 1.65/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7753,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7754,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7753, 7752])).
% 1.65/1.89 tff(7755,plain,
% 1.65/1.89 ((s(s(elem!1)) = s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7754, 45, 7751])).
% 1.65/1.89 tff(7756,plain,
% 1.65/1.89 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7755, 7740])).
% 1.65/1.89 tff(7757,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7758,plain,
% 1.65/1.89 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7759,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7758])).
% 1.65/1.89 tff(7760,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[7759, 7757])).
% 1.65/1.89 tff(7761,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7762,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7761, 7760])).
% 1.65/1.89 tff(7763,plain,
% 1.65/1.89 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7762, 233, 5081])).
% 1.65/1.89 tff(7764,plain,
% 1.65/1.89 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7763, 7743, 7707])).
% 1.65/1.89 tff(7765,plain,
% 1.65/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7766,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7767,plain,
% 1.65/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 1.65/1.89 tff(7768,plain,
% 1.65/1.89 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7767, 45, 7739, 7764])).
% 1.65/1.89 tff(7769,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7770,plain,
% 1.65/1.89 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7771,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7770])).
% 1.65/1.89 tff(7772,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[7771, 7769])).
% 1.65/1.89 tff(7773,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7774,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7773, 7772])).
% 1.65/1.89 tff(7775,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7774, 108, 7768, 7756, 7723, 7699])).
% 1.65/1.89 tff(7776,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(7777,plain,
% 1.65/1.89 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7776, 7684, 7643, 7662, 7653, 5997])).
% 1.65/1.89 tff(7778,plain,
% 1.65/1.89 (r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5077, 7777, 7695])).
% 1.65/1.89 tff(7779,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7778, 7675])).
% 1.65/1.89 tff(7780,plain,(b(elem!1, z) | r(s(s(s(s(s(z))))), s(z)) | r(elem!1, s(z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | b(s(s(s(z))), s(s(s(s(z))))) | (s(s(s(z))) = elem!1) | (~b(z, s(s(s(z))))) | b(s(s(s(z))), s(s(z))) | b(s(s(s(s(z)))), s(s(s(z)))) | (z = elem!1) | b(z, elem!1) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(7781,plain,
% 1.65/1.89 (b(z, elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7780, 7634, 1357, 2854, 6981, 6983, 7000, 5996, 7136, 6975, 3698, 4306, 6998, 6997, 6972])).
% 1.65/1.89 tff(7782,plain,
% 1.65/1.89 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7179, 7781, 6996])).
% 1.65/1.89 tff(7783,plain,
% 1.65/1.89 (~(elem!1 = z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1631, 6998])).
% 1.65/1.89 tff(7784,plain,
% 1.65/1.89 (r(elem!1, z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1037, 7634, 7783])).
% 1.65/1.89 tff(7785,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7786,plain,
% 1.65/1.89 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7787,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7786])).
% 1.65/1.89 tff(7788,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.89 inference(transitivity,[status(thm)],[7787, 7785])).
% 1.65/1.89 tff(7789,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7790,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7789, 7788])).
% 1.65/1.89 tff(7791,plain,
% 1.65/1.89 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7790, 108, 7784, 7001, 7000])).
% 1.65/1.89 tff(7792,plain,
% 1.65/1.89 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[850, 7791, 7782])).
% 1.65/1.89 tff(7793,plain,
% 1.65/1.89 (~(s(s(s(s(z)))) = elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[855, 7782])).
% 1.65/1.89 tff(7794,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7795,plain,
% 1.65/1.89 (((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7796,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7795])).
% 1.65/1.89 tff(7797,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.65/1.89 inference(transitivity,[status(thm)],[7796, 7794])).
% 1.65/1.89 tff(7798,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7799,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7798, 7797])).
% 1.65/1.89 tff(7800,plain,
% 1.65/1.89 (~r(s(s(s(s(z)))), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7799, 108, 7784, 7001, 7000])).
% 1.65/1.89 tff(7801,plain,
% 1.65/1.89 (b(s(s(s(s(z)))), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[860, 7800, 7793])).
% 1.65/1.89 tff(7802,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7803,plain,
% 1.65/1.89 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7804,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7803])).
% 1.65/1.89 tff(7805,plain,
% 1.65/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[7804, 7802])).
% 1.65/1.89 tff(7806,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(7807,plain,
% 1.65/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[7806, 7805])).
% 1.65/1.89 tff(7808,plain,
% 1.65/1.89 (~b(elem!1, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7807, 233, 7801, 7792, 2854])).
% 1.65/1.89 tff(7809,plain,
% 1.65/1.89 (elem!1 = s(z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[965, 7808, 1357])).
% 1.65/1.89 tff(7810,plain,
% 1.65/1.89 (b(z, elem!1) <=> b(z, s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7809])).
% 1.65/1.89 tff(7811,plain,
% 1.65/1.89 (b(z, s(z)) <=> b(z, elem!1)),
% 1.65/1.89 inference(symmetry,[status(thm)],[7810])).
% 1.65/1.89 tff(7812,plain,
% 1.65/1.89 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7811])).
% 1.65/1.89 tff(7813,plain,
% 1.65/1.89 (~b(z, elem!1)),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[6984, 7812])).
% 1.65/1.89 tff(7814,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7781, 7813])).
% 1.65/1.89 tff(7815,plain,(b(s(s(s(z))), s(s(z))) | r(elem!1, s(z)) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(7816,plain,
% 1.65/1.89 (b(s(s(s(z))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7815, 5996, 2854, 1357, 4306, 4303, 1072])).
% 1.65/1.89 tff(7817,plain,
% 1.65/1.89 (~b(z, s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2572, 7816, 6971, 6975])).
% 1.65/1.89 tff(7818,plain,
% 1.65/1.89 (~r(z, s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5891, 7816, 6973, 7000, 4305])).
% 1.65/1.89 tff(7819,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[359, 7818, 7817])).
% 1.65/1.89 tff(7820,plain,(b(s(s(s(z))), s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | b(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(7821,plain,
% 1.65/1.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7820, 4306, 1357, 2854, 4303, 1072])).
% 1.65/1.89 tff(7822,plain,
% 1.65/1.89 (~b(s(s(s(s(z)))), z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3241, 7821, 2854, 1072])).
% 1.65/1.89 tff(7823,plain,
% 1.65/1.89 (r(s(s(s(s(z)))), z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3228, 7822])).
% 1.65/1.89 tff(7824,plain,
% 1.65/1.89 (~b(s(s(s(z))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3374, 7823, 4305, 6971, 6975, 7821])).
% 1.65/1.89 tff(7825,plain,
% 1.65/1.89 (r(s(s(s(z))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[340, 7824])).
% 1.65/1.89 tff(7826,plain,
% 1.65/1.89 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[6170, 108, 4307, 7825, 4305])).
% 1.65/1.89 tff(7827,plain,
% 1.65/1.89 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[462, 7826])).
% 1.65/1.89 tff(7828,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3384, 233, 7827, 7821, 1072, 2854])).
% 1.65/1.89 tff(7829,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | r(elem!1, s(z)) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(7830,plain,
% 1.65/1.89 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7829, 1357, 2854, 1072, 4303])).
% 1.65/1.89 tff(7831,plain,
% 1.65/1.89 (~b(s(z), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3497, 233, 7830, 6971, 2854])).
% 1.65/1.89 tff(7832,plain,
% 1.65/1.89 (r(s(z), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[481, 45, 34, 7831])).
% 1.65/1.89 tff(7833,plain,
% 1.65/1.89 (~b(s(z), s(s(s(z))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3471, 7830, 1072, 2854])).
% 1.65/1.89 tff(7834,plain,
% 1.65/1.89 (r(s(z), s(s(s(z))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[325, 7833])).
% 1.65/1.89 tff(7835,plain,
% 1.65/1.89 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3457, 7830, 1072, 2854])).
% 1.65/1.89 tff(7836,plain,
% 1.65/1.89 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[186, 7835])).
% 1.65/1.89 tff(7837,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3404, 108, 4305, 7836, 7834, 7832])).
% 1.65/1.89 tff(7838,plain,(r(elem!1, s(z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(7839,plain,
% 1.65/1.89 (r(elem!1, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7838, 1072, 2854, 4303])).
% 1.65/1.89 tff(7840,plain,
% 1.65/1.89 (r(elem!1, s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[6541, 6841, 7839])).
% 1.65/1.89 tff(7841,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7842,plain,
% 1.65/1.89 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(7843,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[7842])).
% 1.65/1.89 tff(7844,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.65/1.90 inference(transitivity,[status(thm)],[7843, 7841])).
% 1.65/1.90 tff(7845,plain,
% 1.65/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.65/1.90 inference(quant_inst,[status(thm)],[])).
% 1.65/1.90 tff(7846,plain,
% 1.65/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.65/1.90 inference(modus_ponens,[status(thm)],[7845, 7844])).
% 1.65/1.90 tff(7847,plain,
% 1.65/1.90 ($false),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[7846, 108, 7840, 6861, 6856, 6848])).
% 1.65/1.90 tff(7848,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | b(s(s(z)), s(s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.90 tff(7849,plain,
% 1.65/1.90 (~r(s(s(z)), z)),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[7848, 3344, 4303, 6836, 1072, 2854])).
% 1.65/1.90 tff(7850,plain,
% 1.65/1.90 (b(s(s(z)), z)),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[374, 7849])).
% 1.65/1.90 tff(7851,plain,
% 1.65/1.90 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[6945, 284, 1072, 2854, 2240, 3344, 649])).
% 1.65/1.90 tff(7852,plain,
% 1.65/1.90 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[3374, 284, 2240, 3344, 3517, 204])).
% 1.65/1.90 tff(7853,plain,
% 1.65/1.90 ($false),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[440, 7852, 7851])).
% 1.65/1.90 tff(7854,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.90 tff(7855,plain,
% 1.65/1.90 (~b(s(s(s(z))), s(s(z)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[7854, 204, 4305, 1072, 2854, 7850])).
% 1.65/1.90 tff(7856,plain,
% 1.65/1.90 (r(s(s(s(z))), s(s(z)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[340, 7855])).
% 1.65/1.90 tff(7857,plain,
% 1.65/1.90 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[6170, 108, 6836, 7856, 4305])).
% 1.65/1.90 tff(7858,plain,
% 1.65/1.90 (b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[462, 7857])).
% 1.65/1.90 tff(7859,plain,
% 1.65/1.90 ($false),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[3384, 233, 7858, 204, 1072, 2854])).
% 1.65/1.90 tff(7860,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.90 tff(7861,plain,
% 1.65/1.90 (~b(s(s(s(z))), s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[7860, 6599, 6834, 4303])).
% 1.65/1.90 tff(7862,plain,
% 1.65/1.90 (r(s(s(s(z))), s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[1090, 7861])).
% 1.65/1.90 tff(7863,plain,
% 1.65/1.90 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.65/1.90 inference(rewrite,[status(thm)],[])).
% 1.65/1.90 tff(7864,plain,
% 1.65/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7863])).
% 1.74/1.90 tff(7865,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7864, 4181])).
% 1.74/1.90 tff(7866,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7867,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7866, 7865])).
% 1.74/1.90 tff(7868,plain,
% 1.74/1.90 (~b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7867, 233, 389, 6834, 2854])).
% 1.74/1.90 tff(7869,plain,
% 1.74/1.90 (r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[325, 7868])).
% 1.74/1.90 tff(7870,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7871,plain,
% 1.74/1.90 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7872,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7871])).
% 1.74/1.90 tff(7873,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7872, 7870])).
% 1.74/1.90 tff(7874,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7875,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7874, 7873])).
% 1.74/1.90 tff(7876,plain,
% 1.74/1.90 (~r(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7875, 108, 2240, 7869, 92])).
% 1.74/1.90 tff(7877,plain,
% 1.74/1.90 (b(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[50, 7876])).
% 1.74/1.90 tff(7878,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7879,plain,
% 1.74/1.90 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7880,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7879])).
% 1.74/1.90 tff(7881,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7880, 7878])).
% 1.74/1.90 tff(7882,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7883,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7882, 7881])).
% 1.74/1.90 tff(7884,plain,
% 1.74/1.90 (~r(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7883, 108, 2240, 7869, 92])).
% 1.74/1.90 tff(7885,plain,
% 1.74/1.90 (b(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2414, 7884])).
% 1.74/1.90 tff(7886,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3276, 493, 2240, 5995])).
% 1.74/1.90 tff(7887,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[462, 7886])).
% 1.74/1.90 tff(7888,plain,
% 1.74/1.90 (~b(z, s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5968, 7887, 5920, 6834])).
% 1.74/1.90 tff(7889,plain,
% 1.74/1.90 (r(z, s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[222, 7888])).
% 1.74/1.90 tff(7890,plain,
% 1.74/1.90 (~b(s(s(z)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2398, 284, 7887, 6834])).
% 1.74/1.90 tff(7891,plain,
% 1.74/1.90 (r(s(s(z)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[374, 7890])).
% 1.74/1.90 tff(7892,plain,
% 1.74/1.90 (~b(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4010, 284, 5995, 6834, 7887])).
% 1.74/1.90 tff(7893,plain,
% 1.74/1.90 (r(s(s(s(z))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[244, 7892])).
% 1.74/1.90 tff(7894,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2634, 7893, 7891, 493, 2240])).
% 1.74/1.90 tff(7895,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7896,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7895, 493, 2240])).
% 1.74/1.90 tff(7897,plain,
% 1.74/1.90 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[340, 7896])).
% 1.74/1.90 tff(7898,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7899,plain,
% 1.74/1.90 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7900,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7899])).
% 1.74/1.90 tff(7901,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7900, 7898])).
% 1.74/1.90 tff(7902,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7903,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7902, 7901])).
% 1.74/1.90 tff(7904,plain,
% 1.74/1.90 (~b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7903, 233, 442, 6834, 2854])).
% 1.74/1.90 tff(7905,plain,
% 1.74/1.90 (r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[325, 7904])).
% 1.74/1.90 tff(7906,plain,
% 1.74/1.90 (~r(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4130, 108, 492, 2240, 7905])).
% 1.74/1.90 tff(7907,plain,
% 1.74/1.90 (b(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2414, 7906])).
% 1.74/1.90 tff(7908,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7909,plain,
% 1.74/1.90 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7910,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7909])).
% 1.74/1.90 tff(7911,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7910, 7908])).
% 1.74/1.90 tff(7912,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7913,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7912, 7911])).
% 1.74/1.90 tff(7914,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7913, 233, 442, 7907, 2854, 519])).
% 1.74/1.90 tff(7915,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7916,plain,
% 1.74/1.90 (~b(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7915, 7887, 2854, 7897, 2240])).
% 1.74/1.90 tff(7917,plain,
% 1.74/1.90 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6795, 7916, 92, 7887, 7897, 2854])).
% 1.74/1.90 tff(7918,plain,
% 1.74/1.90 (r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[440, 7917])).
% 1.74/1.90 tff(7919,plain,
% 1.74/1.90 (~r(s(s(z)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4008, 7918, 5995, 7889])).
% 1.74/1.90 tff(7920,plain,
% 1.74/1.90 (b(s(s(z)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[374, 7919])).
% 1.74/1.90 tff(7921,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2503, 7918, 2240, 7897])).
% 1.74/1.90 tff(7922,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[386, 7921])).
% 1.74/1.90 tff(7923,plain,
% 1.74/1.90 (~b(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6822, 233, 5920, 649, 402])).
% 1.74/1.90 tff(7924,plain,
% 1.74/1.90 (r(s(z), s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2414, 7923])).
% 1.74/1.90 tff(7925,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6793, 108, 492, 92, 6647, 7924])).
% 1.74/1.90 tff(7926,plain,((~b(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7927,plain,
% 1.74/1.90 (~b(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7926, 7922, 92, 7897, 7920, 2854])).
% 1.74/1.90 tff(7928,plain,
% 1.74/1.90 (r(s(z), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[260, 7927])).
% 1.74/1.90 tff(7929,plain,
% 1.74/1.90 (r(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[50, 7916])).
% 1.74/1.90 tff(7930,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7931,plain,
% 1.74/1.90 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7932,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7931])).
% 1.74/1.90 tff(7933,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7932, 7930])).
% 1.74/1.90 tff(7934,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(7935,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[7934, 7933])).
% 1.74/1.90 tff(7936,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7935, 108, 2240, 92, 7929, 7928])).
% 1.74/1.90 tff(7937,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(7938,plain,
% 1.74/1.90 (~r(z, s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[7937, 2240, 92, 2854])).
% 1.74/1.90 tff(7939,plain,
% 1.74/1.90 (b(z, s(s(z)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[359, 7938])).
% 1.74/1.90 tff(7940,plain,
% 1.74/1.90 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(7941,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[7940])).
% 1.74/1.90 tff(7942,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[7941, 483])).
% 1.74/1.90 tff(7943,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(7944,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7943, 7942])).
% 1.74/1.91 tff(7945,plain,
% 1.74/1.91 (~b(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7944, 233, 7939, 7885, 7877])).
% 1.74/1.91 tff(7946,plain,
% 1.74/1.91 (r(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[128, 7945])).
% 1.74/1.91 tff(7947,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7948,plain,
% 1.74/1.91 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7949,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[7948])).
% 1.74/1.91 tff(7950,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[7949, 7947])).
% 1.74/1.91 tff(7951,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(7952,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7951, 7950])).
% 1.74/1.91 tff(7953,plain,
% 1.74/1.91 (~b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7952, 233, 7939, 7885, 7877])).
% 1.74/1.91 tff(7954,plain,
% 1.74/1.91 (r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[260, 7953])).
% 1.74/1.91 tff(7955,plain,
% 1.74/1.91 (~b(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1188, 233, 389, 5920, 6834])).
% 1.74/1.91 tff(7956,plain,
% 1.74/1.91 (r(z, s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[222, 7955])).
% 1.74/1.91 tff(7957,plain,
% 1.74/1.91 (~r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[986, 7954, 92, 7956])).
% 1.74/1.91 tff(7958,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[244, 7957])).
% 1.74/1.91 tff(7959,plain,
% 1.74/1.91 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3176, 7958, 5920, 92, 7954, 7946])).
% 1.74/1.91 tff(7960,plain,
% 1.74/1.91 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3933, 7959])).
% 1.74/1.91 tff(7961,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7962,plain,
% 1.74/1.91 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7963,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[7962])).
% 1.74/1.91 tff(7964,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[7963, 7961])).
% 1.74/1.91 tff(7965,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(7966,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7965, 7964])).
% 1.74/1.91 tff(7967,plain,
% 1.74/1.91 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7966, 233, 7885, 7960, 7877])).
% 1.74/1.91 tff(7968,plain,
% 1.74/1.91 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[535, 45, 532, 7967])).
% 1.74/1.91 tff(7969,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7142, 108, 7956, 5995, 7954])).
% 1.74/1.91 tff(7970,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4293, 7969])).
% 1.74/1.91 tff(7971,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7972,plain,
% 1.74/1.91 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7973,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[7972])).
% 1.74/1.91 tff(7974,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[7973, 7971])).
% 1.74/1.91 tff(7975,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(7976,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7975, 7974])).
% 1.74/1.91 tff(7977,plain,
% 1.74/1.91 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7976, 233, 7885, 7960, 7970])).
% 1.74/1.91 tff(7978,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[745, 7977])).
% 1.74/1.91 tff(7979,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7980,plain,
% 1.74/1.91 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7981,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[7980])).
% 1.74/1.91 tff(7982,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[7981, 7979])).
% 1.74/1.91 tff(7983,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(7984,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7983, 7982])).
% 1.74/1.91 tff(7985,plain,
% 1.74/1.91 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7984, 233, 7885, 7960, 7877])).
% 1.74/1.91 tff(7986,plain,
% 1.74/1.91 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4247, 45, 7985])).
% 1.74/1.91 tff(7987,plain,
% 1.74/1.91 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7986, 4096])).
% 1.74/1.91 tff(7988,plain,
% 1.74/1.91 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6489, 7970, 2854, 7877])).
% 1.74/1.91 tff(7989,plain,
% 1.74/1.91 (r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[440, 7988])).
% 1.74/1.91 tff(7990,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7991,plain,
% 1.74/1.91 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(7992,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[7991])).
% 1.74/1.91 tff(7993,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[7992, 7990])).
% 1.74/1.91 tff(7994,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(7995,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[7994, 7993])).
% 1.74/1.91 tff(7996,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7995, 108, 7989, 7987, 7978, 7968])).
% 1.74/1.91 tff(7997,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(7998,plain,
% 1.74/1.91 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7997, 6599, 7862, 4305])).
% 1.74/1.91 tff(7999,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[386, 7998])).
% 1.74/1.91 tff(8000,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4326, 7999, 4305, 7862])).
% 1.74/1.91 tff(8001,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[440, 8000])).
% 1.74/1.91 tff(8002,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6376, 7999, 5920, 5995, 6834, 4305, 7862])).
% 1.74/1.91 tff(8003,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[462, 8002])).
% 1.74/1.91 tff(8004,plain,
% 1.74/1.91 (~r(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7937, 4305, 7862, 6599])).
% 1.74/1.91 tff(8005,plain,
% 1.74/1.91 (b(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[359, 8004])).
% 1.74/1.91 tff(8006,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2572, 8001, 5920, 8005])).
% 1.74/1.91 tff(8007,plain,
% 1.74/1.91 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[340, 8006])).
% 1.74/1.91 tff(8008,plain,
% 1.74/1.91 (~b(s(s(z)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[7915, 8007, 6599, 8003, 4305])).
% 1.74/1.91 tff(8009,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6795, 8008, 8007, 7862, 8003, 8001, 6599])).
% 1.74/1.91 tff(8010,plain,(b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8011,plain,
% 1.74/1.91 (~b(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[366, 233, 8010, 5920, 6834])).
% 1.74/1.91 tff(8012,plain,
% 1.74/1.91 (r(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[374, 8011])).
% 1.74/1.91 tff(8013,plain,
% 1.74/1.91 (~b(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[347, 233, 8010, 5920, 6834])).
% 1.74/1.91 tff(8014,plain,
% 1.74/1.91 (r(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[359, 8013])).
% 1.74/1.91 tff(8015,plain,
% 1.74/1.91 (~r(s(s(z)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4022, 680, 8014, 5995])).
% 1.74/1.91 tff(8016,plain,
% 1.74/1.91 (b(s(s(z)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[50, 8015])).
% 1.74/1.91 tff(8017,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.91 tff(8018,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8019,plain,
% 1.74/1.91 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(8020,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[8019])).
% 1.74/1.91 tff(8021,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[8020, 8018])).
% 1.74/1.91 tff(8022,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(8023,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 1.74/1.91 tff(8024,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8023, 108, 493, 680, 3244, 8017])).
% 1.74/1.91 tff(8025,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8026,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8025, 680, 8014, 5995])).
% 1.74/1.91 tff(8027,assumption,(s(s(z)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.91 tff(8028,plain,
% 1.74/1.91 (s(s(s(s(s(z))))) = s(s(z))),
% 1.74/1.91 inference(symmetry,[status(thm)],[8027])).
% 1.74/1.91 tff(8029,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[532, 8028])).
% 1.74/1.91 tff(8030,plain,(~(s(s(z)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8031,assumption,(~b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.91 tff(8032,assumption,(~r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.91 tff(8033,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4247, 45, 8032, 8031, 8030])).
% 1.74/1.91 tff(8034,plain,(b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8035,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8034, 8026])).
% 1.74/1.91 tff(8036,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.91 tff(8037,plain,
% 1.74/1.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6047, 284, 8010, 8012, 8014])).
% 1.74/1.91 tff(8038,plain,
% 1.74/1.91 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[598, 8037])).
% 1.74/1.91 tff(8039,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3444, 8012, 5995, 8014])).
% 1.74/1.91 tff(8040,plain,
% 1.74/1.91 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[440, 8039])).
% 1.74/1.91 tff(8041,plain,
% 1.74/1.91 (~r(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5491, 284, 5995, 8040, 8014])).
% 1.74/1.91 tff(8042,plain,
% 1.74/1.91 (b(s(s(s(z))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[244, 8041])).
% 1.74/1.91 tff(8043,plain,
% 1.74/1.91 (~b(s(z), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2986, 1072, 8010, 519])).
% 1.74/1.91 tff(8044,plain,
% 1.74/1.91 (r(s(z), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2414, 8043])).
% 1.74/1.91 tff(8045,plain,
% 1.74/1.91 (~b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6092, 1072, 5920, 272])).
% 1.74/1.91 tff(8046,plain,
% 1.74/1.91 (r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[260, 8045])).
% 1.74/1.91 tff(8047,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2971, 108, 8012, 8014, 8046, 8044])).
% 1.74/1.91 tff(8048,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(8049,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8048, 8042, 519])).
% 1.74/1.91 tff(8050,plain,
% 1.74/1.91 (r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1090, 8049])).
% 1.74/1.91 tff(8051,plain,
% 1.74/1.91 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[667, 8042, 5920, 8010])).
% 1.74/1.91 tff(8052,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[386, 8051])).
% 1.74/1.92 tff(8053,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8054,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8055,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8054, 8053])).
% 1.74/1.92 tff(8056,plain,
% 1.74/1.92 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8055, 108, 8052, 8050, 8038])).
% 1.74/1.92 tff(8057,plain,
% 1.74/1.92 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[579, 45, 576, 8056])).
% 1.74/1.92 tff(8058,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8059,plain,
% 1.74/1.92 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8060,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8059])).
% 1.74/1.92 tff(8061,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8060, 8058])).
% 1.74/1.92 tff(8062,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8063,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8062, 8061])).
% 1.74/1.92 tff(8064,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8063, 108, 8052, 8050, 8038])).
% 1.74/1.92 tff(8065,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[745, 8064])).
% 1.74/1.92 tff(8066,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8067,plain,
% 1.74/1.92 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8068,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8067])).
% 1.74/1.92 tff(8069,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8068, 8066])).
% 1.74/1.92 tff(8070,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8071,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8070, 8069])).
% 1.74/1.92 tff(8072,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8071, 233, 8040, 8065, 8057, 8036])).
% 1.74/1.92 tff(8073,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8074,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8073, 8035, 8016])).
% 1.74/1.92 tff(8075,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[340, 8074])).
% 1.74/1.92 tff(8076,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2510, 8075, 8012, 680])).
% 1.74/1.92 tff(8077,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[386, 8076])).
% 1.74/1.92 tff(8078,plain,
% 1.74/1.92 (~r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[703, 8075, 8014, 8012])).
% 1.74/1.92 tff(8079,plain,
% 1.74/1.92 (b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[244, 8078])).
% 1.74/1.92 tff(8080,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[667, 8079, 8077, 5920, 8010])).
% 1.74/1.92 tff(8081,plain,(~r(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8082,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[462, 8081])).
% 1.74/1.92 tff(8083,plain,
% 1.74/1.92 (~b(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5968, 8082, 5920, 6834])).
% 1.74/1.92 tff(8084,plain,
% 1.74/1.92 (r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[222, 8083])).
% 1.74/1.92 tff(8085,plain,
% 1.74/1.92 ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6148, 8084, 5995])).
% 1.74/1.92 tff(8086,plain,
% 1.74/1.92 (~r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8085, 52])).
% 1.74/1.92 tff(8087,plain,
% 1.74/1.92 (b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[260, 8086])).
% 1.74/1.92 tff(8088,plain,
% 1.74/1.92 ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2126, 8012])).
% 1.74/1.92 tff(8089,plain,
% 1.74/1.92 (~r(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8088, 52, 2051])).
% 1.74/1.92 tff(8090,plain,
% 1.74/1.92 (b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[128, 8089])).
% 1.74/1.92 tff(8091,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3364, 8082, 6834, 8040])).
% 1.74/1.92 tff(8092,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[340, 8091])).
% 1.74/1.92 tff(8093,plain,
% 1.74/1.92 (~r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[703, 8092, 8014, 8012])).
% 1.74/1.92 tff(8094,plain,
% 1.74/1.92 (b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[244, 8093])).
% 1.74/1.92 tff(8095,plain,
% 1.74/1.92 (~b(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6309, 233, 8094, 8090, 8087])).
% 1.74/1.92 tff(8096,plain,
% 1.74/1.92 (r(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[325, 8095])).
% 1.74/1.92 tff(8097,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[450, 8082, 6834, 8010])).
% 1.74/1.92 tff(8098,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[386, 8097])).
% 1.74/1.92 tff(8099,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8100,plain,
% 1.74/1.92 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8101,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8100])).
% 1.74/1.92 tff(8102,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8101, 8099])).
% 1.74/1.92 tff(8103,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8104,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8103, 8102])).
% 1.74/1.92 tff(8105,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8104, 108, 8098, 8092, 8096, 52])).
% 1.74/1.92 tff(8106,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8107,plain,
% 1.74/1.92 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8106, 51])).
% 1.74/1.92 tff(8108,plain,
% 1.74/1.92 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1122, 8107])).
% 1.74/1.92 tff(8109,plain,
% 1.74/1.92 (b(s(s(z)), s(z)) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6795, 8092, 8082, 8040])).
% 1.74/1.92 tff(8110,plain,
% 1.74/1.92 (~r(s(s(s(z))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8109, 8108, 1])).
% 1.74/1.92 tff(8111,plain,
% 1.74/1.92 (b(s(s(s(z))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1090, 8110])).
% 1.74/1.92 tff(8112,plain,
% 1.74/1.92 ((~b(s(s(s(z))), s(z))) | (~b(s(z), z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6092, 5920, 8094])).
% 1.74/1.92 tff(8113,plain,
% 1.74/1.92 (~b(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8112, 8111])).
% 1.74/1.92 tff(8114,plain,
% 1.74/1.92 (r(s(z), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[260, 8113])).
% 1.74/1.92 tff(8115,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2963, 108, 8012, 8014, 51, 8114])).
% 1.74/1.92 tff(8116,plain,(b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8117,plain,
% 1.74/1.92 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8118,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8117])).
% 1.74/1.92 tff(8119,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8118, 7248])).
% 1.74/1.92 tff(8120,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8121,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8120, 8119])).
% 1.74/1.92 tff(8122,plain,
% 1.74/1.92 (~b(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8121, 233, 5920, 8094, 8087])).
% 1.74/1.92 tff(8123,plain,
% 1.74/1.92 (r(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[325, 8122])).
% 1.74/1.92 tff(8124,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8104, 108, 8098, 8092, 8123, 52])).
% 1.74/1.92 tff(8125,plain,(~r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8126,plain,
% 1.74/1.92 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1122, 8125])).
% 1.74/1.92 tff(8127,plain,
% 1.74/1.92 ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6489, 8040])).
% 1.74/1.92 tff(8128,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8127, 8126, 8116])).
% 1.74/1.92 tff(8129,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4293, 8128])).
% 1.74/1.92 tff(8130,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8131,plain,
% 1.74/1.92 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(8132,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[8131])).
% 1.74/1.92 tff(8133,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[8132, 8130])).
% 1.74/1.92 tff(8134,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(8135,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[8134, 8133])).
% 1.74/1.92 tff(8136,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[8135, 108, 8098, 8092, 2337, 8129])).
% 1.74/1.92 tff(8137,plain,(~r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(8138,plain,
% 1.74/1.92 (b(s(z), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[325, 8137])).
% 1.74/1.92 tff(8139,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2170, 233, 8010, 8094, 8138, 8116])).
% 1.74/1.92 % SZS output end Proof
% 1.74/1.93 % E exiting
%------------------------------------------------------------------------------